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 »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 »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 »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 »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 »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 - ${2}/{13}$ = ${11}/{13}$
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Probability Model Questions Set 1 Online Quiz
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