Probability Tips & Practice Questions for SBI PO Prelims

SBI PO prelims exam is about to commence in a few days from now and it’s high time that the aspirants must revise for this upcoming examination. Quantitative Aptitude is one topic which requires rigorous practice and each and every concept is to be studied and practiced well. We are collating different topics/concepts of quant and sharing the tips and practice questions. In this article we will be discussing Probability Tips & Practice Questions for SBI PO Prelims. 

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Probability Tips & Practice Questions for SBI PO Prelims

Probability:

Questions based on probability can be asked in the following ways
i) To find the probability of an event

ii) To find the probability of a combination of different events

iii) To find the difference in the probability of occurrence of two or more different events.

Basics:

Probability is the measure that tells us how likely is an event to happen.

Let ‘P’ be the value of probability of occurrence of an event.

Then, 0 ≤ P ≤ 1

If an event is a certain event, i.e. if it is sure that the event is going to occur, then probability of the given event is ‘1’.

If an event is an impossible event i.e. if it is sure that the event cannot occur, then probability of occurrence of the given event is ‘0’.

Probability of two related events:

Consider the event of writing an examination. The given event has only two possible outcomes: passing the examination and failing the examination.

Let ‘P’ be the probability of passing the examination and let ‘Q’ be the probability of failing the examination. Then (P + Q) = 1.

Following the same principle, if ‘P’ be the probability of a person passing the exam, then the probability of the person failing the exam is (1 – P).

Classical definition of probability = Number of favorable events in the outcome ÷ total number of events in the outcome

The set of all possible events is called the sample space.

The set of events which is of interest to us is called the event.

Then, probability of a given event = n(E) ÷ n(S)

Bias – When the probability of a certain event is different than the usually expected probability, then the occurrence of the event is said to be biased. For example, while tossing a coin, if the probability of getting a head and a tail are not the equal, then the coin is said to be a biased coin.

Let ‘E₁’ and ‘E₂’ be two different events where the probability of occurrence of ‘E₁’ and ‘E₂’ is ‘p’ and ‘q’, respectively

Then, the probability of occurrence of both ‘E₁’ and ‘E₂’ = (p × q).

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Probability Practice Questions

Question 1: A bag contains red, blue and green balls in the ratio of 2:4:5 respectively. Two balls are randomly drawn from the bag and the probability that both the balls drawn are blue in colour is 1/8. Find the total number of balls in the bag.

A) 22

B) 33

C) 44

D) 55

E) 88

Question 2: A bag contains 5 grey, 4 blue and 3 red balls. A man draws three balls randomly. What would be the probability that all balls are of different colours?

A) 4/45

B) 12/19

C) 3/47

D) 3/11

E) 9/22

Question 3: A fruit seller has three types of mangoes in his bucket viz. Dasheri, Langra and Chaunsa. The probability of selling one Dasheri mango is 3/8, while the probability of selling one Langra mango is 2/7. If he has total 38 Chaunsa mangoes, then what is the total number of mangoes in his bucket?

A) 56

B) 72

C) 96

D) 112

E) 124

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Question 4: A bag contains (x + 3) red, ‘x’ green and (x + 1) blue balls. The probability of getting two blue balls from the bag is 1/12. If three balls are selected from the bag at random, then find the probability that all the balls are of different colour.

A) 1/4

B) 3/4

C) 1/2

D) 1/8

E) None of these

Question 5: A box contains 5 red, 3 green and 4 black balls. Four balls are taken out from the box at random, what is the probability of getting exactly two red, 1 green and 1 black ball?

A) 8/33

B) 5/13

C) 11/31

D) 7/39

E) None of these

Question 6: There are cubes of three colours red, blue and white in a bag. The probability of picking a white cube from the bag is 1/3. If the number of red cubes is 50% less than the number of blue cubes then find the probability of picking a red cube at random.

A) 2/7

B) 3/5

C) 1/4

D) 2/9

E) Cannot be determined

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Question 7: A bag contains 2 green, 4 orange and some red balls. If two balls are selected from the bag at random then the probability of getting an orange and a red ball is 4/11. Find the total number of balls in the bag.

A) 12

B) 11

C) 13

D) 10

E) Cannot be determined

Question 8: A box has 4 red, 8 blue and 5 black balls. If three balls are to be picked, then find the probability that all the three balls are of the same colour.

A) 4/67

B) 11/69

C) 9/71

D) 7/68

E) None of these

Question 9: The probability of picking a red ball out of balls of three different colours in a bag i.e. blue, black and red is 6/13. The number of black balls is 25% less than that of the blue balls. If the number of red balls in the bag is 24, then find the number of blue balls.

A) 18

B) 15

C) 16

D) 12

E) 20

Question 10: A bag contains 3 blue, 4 black, and 2 yellow balls. A person draws 2 balls at random from the bag. What will be the probability that both ball are of different colours?

A) 13/18

B) 7/19

C) 16/21

D) 9/16

E) 11/21

प्रश्न 1: एक बैग में red, blue और green balls का अनुपात क्रमशः 2:4:5 है | बैग में से कोई भी दो balls निकाली गयी और दोनों balls के blue colour के होने की सम्भावना 1/8 है | bag में कुल balls की संख्या ज्ञात करें ?

A) 22

B) 33

C) 44

D) 55

E) 88

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प्रश्न 2: एक बैग में 5 grey, 4 blue और 3 red balls है, एक व्यक्ति कोई भी तीन balls निकालता है, तो सभी balls के अलग अलग रंग के होने की प्रायिकता कितनी हो सकती है ?

A) 4/45

B) 12/19

C) 3/47

D) 3/11

E) 9/22

प्रश्न 3: एक फल विक्रेता के पास अपनी बाल्टी में तीन प्रकार के mangoes हैं जो कि Dasheri, Langra और Chaunsa हैं। एक Dasheri mango को बेचने की प्रायिकता 3/8 है, जबकि एक Langra mango को बेचने की प्रायिकता 2/7 है। यदि उसके पास कुल 38 Chaunsa mangoes हैं, तो उसकी बाल्टी में mangoes की कुल संख्या कितनी है?

A) 56

B) 72

C) 96

D) 112

E) 124

प्रश्न 4: एक बैग में ((x + 3) red, ‘x’ green and (x + 1) blue balls हैं। बैग से दो blue balls प्राप्त करने की प्रायिकता 1/12 है। यदि तीन balls को बैग से यादृच्छिक रूप से चुना जाता है, तो सभी balls के अलग-अलग रंग के होने की प्रायिकता ज्ञात करें|

A) 1/4

B) 3/4

C) 1/2

D) 1/8

E) इनमें से कोई नहीं

प्रश्न 5: एक box में 5 red, 3 green और 4 black balls होते हैं। box में यादृच्छिक रूप से चार balls निकाली जाती हैं, दो red, 1 green और 1 black ball होने की प्रायिकता ज्ञात करें?

A) 8/33

B) 5/13

C) 11/31

D) 7/39

E) इनमें से कोई नहीं

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प्रश्न 6: एक बैग में तीन रंग के घन है अर्थात red, blue और white।बैग से एक white घन चुनने की प्रायिकता 1/3 है।यदि red घन की संख्या blue घन की संख्या से 50% कम है तो यादृच्छिक रूप से एक red घन चुनने की प्रायिकता ज्ञात करें?

A) 2/7

B) 3/5

C) 1/4

D) 2/9

E) निर्धारित नहीं किया जा सकता

प्रश्न 7: एक बैग में 2 green, 4 orange और कुछ red balls होती हैं। यदि दो balls को बैग से यादृच्छिक रूप से चुना जाता है तो orange and एक red ball प्राप्त करने की प्रायिकता 4/11 है। बैग में balls की कुल संख्या ज्ञात करें?

A) 12

B) 11

C) 13

D) 10

E) निर्धारित नहीं किया जा सकता

प्रश्न 8: एक box में 4 red, 8 blue और 5 black balls हैं।यदि तीन balls का चयन किया जाना है तो इस बात की प्रायिकता ज्ञात करें कि तीनों balls समान colour की हैं।

A) 4/67

B) 11/69

C) 9/71

D) 7/68

E) इनमें से कोई नहीं

प्रश्न 9: एक bag में तीन रंग के balls हैं अर्थात blue, black और red और bag में से एक red ball को चुनने की प्रायिकता 6/13 है|Black balls की संख्या blue balls की संख्या से 25% कम है|यदि bag में red balls की संख्या 24 है, तो blue balls की संख्या ज्ञात करें|

A) 18

B) 15

C) 16

D) 12

E) 20

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प्रश्न 10: एक बैग में 3 blue, 4 black, और 2 yellow balls होते हैं। एक व्यक्ति बैग से यादृच्छिक रूप से 2 balls निकालता है। इस बात की कितनी प्रायिकता होगी कि दोनों ball अलग-अलग रंग की हैं?

A) 13/18

B) 7/19

C) 16/21

D) 9/16

E) 11/21

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ANSWER KEYS and SOLUTIONS:

Solution 1: B)

Let the number of red, blue and green balls in the bag are 2x, 4x and 5x respectively.

Total number of balls in the bag = 2x + 4x + 5x = 11x

So according to question: ^4xC₂/^11xC₂ = 1/8

4x (4x – 1)/ 11x (11x – 1) = 1/8

(16x – 4)/ (121x – 11) = 1/8

128x – 32 = 121x – 11

7x = 21, x = 3

So the total number of balls in the bag = 33

Hence, option b.

Solution 2: D)

Total number of ways of drawing 3 balls = ¹²C₃ = 220

Total number of ways drawing balls of different colour = ⁵C₁×⁴C₁׳C₁ = 60

Therefore, probability of drawing different colour = 60/220 = 3/11

Hence, option d.

Solution 3: D)

Probability of selling a Chaunsa mango = 1 – (3/8 + 2/7) = 1 – (21 + 16)/56 = (56 – 37)/56 = 19/56

Therefore, total number of mangoes in his bucket = 38 × (56/19) = 112

Hence, option d.

Solution 4: A)

Total number of balls in the bag = x + 3 + x + x + 1 = 3x + 4

According to question;

^{(x + 1)}C₂/^{(3x + 4)}C₂ = 1/12

{(x + 1) × x}/{(3x + 4)(3x + 3)} = 1/12

Or, {(x + 1) × x}/{3(3x + 4)(x + 1)} = 1/12

Or, 4x = 3x + 4

So, x = 4

Number of red balls in the bag = x + 3 = 7

Number of green balls in the bag = x = 4

Number of blue balls in the bag = x + 1 = 4 + 1 = 5

Total number of balls in the bag = 3x + 4 = 16

Desired probability = (⁷C₁ × ⁴C₁ × ⁵C₁)/ ¹⁶C₃ = (7 × 4 × 5 × 3 × 2)/(16 × 15 × 14) = 1/4

Hence, option a.

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Solution 5: A)

Total number of balls = 5 + 3 + 4 = 12

Desired probability = (⁵C₂ × ³C₁ × ⁴C₁)/¹²C₄ = 8/33

Hence, option a.

Solution 6: D)

Let total number of cubes be 3x

Therefore, number of white cubes = x

Number of red and blue cubes = 3x – x = 2x

Number of red cubes = 2x/1.5 × 1/2 = 2x/3

Required probability = (2x/3)/3x = 2/9

Hence, option d.

Solution 7: E)

Let the number of red balls in the bag is ‘x’

Total number of balls in the bag = (x + 6)

According to question;

(^xC₁ × ⁴C₁)/ ^{(x + 6)}C₂ = 4/11

8x/(x + 6)(x + 5) = 4/11

22x = x² + 11x + 30

x² – 11x + 30 = 0

x² – 6x – 5x + 30 = 0

x(x – 6) – 5(x – 6) = 0

(x – 5)(x – 6) = 0

x = 5 or x = 6

So, total number of balls in the bag can be 11 or 12

Hence, option e.

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Solution 8: D)

Required probability = (⁴C₃ + ⁸C₃ + ⁵C₃) ÷ ¹⁷C₃

= (4 + 56 + 10)/680 = 7/68

Hence, option d.

Solution 9: C)

Let the total number of balls be 13x

Therefore, number of red balls 6x

Or, 6x = 24

Or, x = 4

Therefore, number of blue and black balls = 13x – 6x = 7x = 28

Number of blue balls = 28/1.75 = 16

Number of black balls = 0.75 × 16 = 12

Hence, option c.

Solution 10: A)

Required probability = {(³C₁ × ⁴C₁) + (⁴C₁ × ²C₁) + (³C₁ × ²C₁)}/⁹C₂ = (12 + 8 + 6)/36 = 13/18

Hence, option a.

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This brings us to the end of Probability Tips & Practice Questions for SBI PO Prelims. Its time to speed up your preparation/revision for the upcoming SBI PO prelims examination.

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