Probability Model Questions Set 1 Practice Questions Answers Test with Solutions & More Shortcuts

Probability PRACTICE TEST [1 - EXERCISES]

Probability Model Questions Set 1

Question : 6

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 : 7

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 : 8

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 : 9

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

A box contains 2 blue caps, 4 red caps, 5 green caps and 1 yellow cap.


If two caps are picked at random, what is the probability that at least one is red ?

a) $16/21$

b) $7/19$

c) $1/3$

d) $19/33$

e) None of these

Answer: (d)

Required probability = 1- ${^8C_2}/{^{12}C_2}$ = 1- ${28}/{66}$ = ${38}/{66}$ = ${19}/{33}$

Question : 10

Out of 15 students studying in a class, 7 are from Maharashtra, 5 from Karnataka and 3 from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?

a) $11/13$

b) $51/15$

c) $12/13$

d) $100/15$

e) None of these

Answer: (a)

P(At least one from Karnataka) = 1 – P(No one from Karnataka)

= 1-${{^10}C_4}/{^{15}C_4}$ = 1 - ${10 × 9 × 8 × 7}/{15 × 14 × 13 × 12}$ = 1 - ${2}/{13}$ = ${11}/{13}$

IMPORTANT quantitative aptitude EXERCISES

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