Probability Model Questions Set 1 Section-Wise Topic Notes With Detailed Explanation And Example Questions

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The following question based on Probability topic of quantitative aptitude

Questions : A dice is thrown. What is the probability that the number shown on the dice is not divisible by 3?

(a) $2/3$

(b) $2/5$

(c) $1/3$

(d) $1/4$

e) None of these

The correct answers to the above question in:

Answer: (a)

S = {1, 2, 3, 4, 5, 6}; n(S) = 6

E(not divisible by 3) = 1, 2, 4, 5}, n(E) = 4

∴ P(not divisible by 3) = $4/6$ = $2/3$

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Question : 1

Directions :
Study the given information carefully and answer the questions that follow.

A basket contains 4 red, 5 blue and 3 green marbles.


If three marbles are picked at random, what is the probability that at least one is blue ?

a) $37/44$

b) $7/44$

c) $7/12$

d) $5/12$

e) None of these

Answer: (a)

Total possible result = n(S) = $^{12} C_3$.

= ${12 × 11 × 10}/{1 × 2 × 3}$ = 220 Total number of event = n(E)

Except blue marbles, selection of 3 marbles out of 7 marbles

= $^{7}C_3$ = ${7 × 6 × 5}/{1 × 2 × 3}$ = 35

∴ Required probability = $(1 -{35}/{220}) = (1 - {7}/{44})$ = ${37}/{44}$

Question : 2

3 digits are chosen at random from 1,2,3,4,5,6,7,8 and 9 without repeating any digit. What is the probability that their product is odd?

a) $5/108$

b) $8/42$

c) $2/3$

d) $5/42$

e) $9/42$

Answer: (d)

Let E be the event of selecting the three numbers such that their product is odd and S be the sample space.

For the product to be odd, 3 numbers chosen must be odd.

∴ n(E) = $^5C_3$

n(S) = $^9C_3$

∴ P (E) = ${n(E)}/{n(S)}$ = ${^5C_3}/{^9C_3}$ = ${5}/{42}$

Question : 3

There are 4 boys and 4 girls. They sit in a row randomly. What is the chance that all the girls do not sit together?

a) $13/14$

b) $15/16$

c) $12/13$

d) $14/15$

e) None of these

Answer: (a)

Question : 4

Directions :
Study the given information carefully and answer the questions that follow.

A basket contains 4 red, 5 blue and 3 green marbles.


If two marbles are drawn at random, what is the probability that both are red ?

a) $1/2$

b) $1/6$

c) $3/7$

d) $2/11$

e) None of these

Answer: (e)

Total possible result n(S) = $^{12}C_{2}$ = ${12 × 11}/{1 × 2}$ = 66

Total number of event = n(E) $^4 C _2$ = ${4 × 3}/{1 × 2}$ = 6

∴ Required probability = ${n(E)}/{n(S)}$ = $6/{66}$ = $1/{11}$

Question : 5

In a box carrying one dozen of oranges, one-third have become bad. If 3 oranges are taken out from the box at random, what is the probability that at least one orange out of the three oranges picked up is good?

a) $54/55$

b) $3/55$

c) $1/55$

d) $45/55$

e) None of these

Answer: (a)

P(At least one good) = 1 – P(All bad)

= 1 - ${{^4C_3}/{^12C_3}}$ = 1 - ${4/{220}}$ = 1 -${1/{55}}$= ${54}/{55}$

Question : 6

A basket contains three blue and four red balls. If three balls are drawn at random from the basket, what is the probability that all the three are either blue or red ?

a) $1/7$

b) $3/28$

c) 1

d) $3/14$

e) None of these

Answer: (e)

Probability to be a Blue = ${^3C_3}/{^7C_3}$

Probability to be a Red = ${^4 C_3}/{^7C_3}$

Required probability = ${^3 C_3}/{^7 C_3}$ + ${^4 C_3}/{^7C_3}$ = $2/{35}$

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Probability Model Questions Set 1

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