CRE 1 - Basics | Modern Math - Probability

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1. CRE 1 - Basics | Modern Math - Probability

A single letter is selected from the word ‘ELEPHANT’ at random. Find the probability that it is a vowel.

(a)
3/8
(b)
1/4
(c)
1/8
(d)
None of these

2. CRE 1 - Basics | Modern Math - Probability

A number selected from the first 100 natural numbers at random. Find the probability that it is a perfect square.

(a)
11/100
(b)
9/100
(c)
1/10
(d)
None of these

3. CRE 1 - Basics | Modern Math - Probability

3 electric bulbs are to be fitted in a room. The bulbs are chosen at random from 10 bulbs having 6 functioning bulbs. Find the probability that the room gets lighted.

(a)
7/30
(b)
29/30
(c)
1/30
(d)
None of these

Answer: Option B

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Explanation :

There are 6 functioning bulbs and 4 defected bulbs.

P (room is lighted) = 1 – P (room is not lighted)

P (room is not lighted) = P (choosing all 3 defected bulbs)

Total Number of ways of choosing bulbs = ¹⁰C₃

Number of ways of choosing defected bulbs = ⁴C₃

∴ P (room is not lighted) = ⁴C₃/¹⁰C₃ = $\frac{4 \times 3 \times 2}{10 \times 9 \times 8}$ = 1/30

∴ P (room is lighted) = 1 – 1/30 = 29/30

Hence, option (b).

4. CRE 1 - Basics | Modern Math - Probability

A man and a woman appear in an interview for two vacancies in the same post. The odds in favor of the man’s selection are 1 : 2 & the odds against the woman’s rejection are 1 : 3. Find the probability that neither of them is selected.

(a)
1/2
(b)
1/12
(c)
1/4
(d)
None of these

5. CRE 1 - Basics | Modern Math - Probability

A number is chosen at random from the first 75 natural numbers. Find the probability that it is either a multiple of 5 or a multiple of 7.

(a)
10/75
(b)
25/75
(c)
23/75
(d)
15/75

Answer the next 5 questions based on the information given below:

3 persons – A, B & C work independently on a problem. The respective probabilities that they will solve it are $\frac{1}{3}$ , $\frac{1}{4}$ and $\frac{1}{5}$ .

6. CRE 1 - Basics | Modern Math - Probability

Find the probability that the problem will not be solved.

(a)
1/60
(b)
2/5
(c)
3/5
(d)
13/30

Answer: Option B

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Explanation :

P (problem will be not solved) = P (A doesn’t solve) × P (B doesn’t solve) × P (C doesn’t solve).

∴ P (problem will not be solved) = $(1 - \frac{1}{3}) (1 - \frac{1}{4}) (1 - \frac{1}{5})$ = $\frac{2}{3} \times \frac{3}{4} \times \frac{4}{5}$ = $\frac{2}{5}$

Hence, option (b).

7. CRE 1 - Basics | Modern Math - Probability

Find the probability that the problem will be solved.

(a)
1/60
(b)
2/5
(c)
3/5
(d)
13/30

Answer: Option C

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Explanation :

P (problem will be solved) = 1 – P (problem will not be solved)

∴ P (problem will not be solved) = $(1 - \frac{1}{3}) (1 - \frac{1}{4}) (1 - \frac{1}{5})$ = $\frac{2}{3} \times \frac{3}{4} \times \frac{4}{5}$ = $\frac{2}{5}$

⇒ P (problem will be solved) = 1 – P (problem will not be solved) = $1 - \frac{2}{5}$ = $\frac{3}{5}$

Hence, option (c).

8. CRE 1 - Basics | Modern Math - Probability

Find the probability that each of them will solve it.

(a)
1/60
(b)
2/5
(c)
3/5
(d)
13/30

9. CRE 1 - Basics | Modern Math - Probability

Find the probability that exactly one of them will solve it.

(a)
1/60
(b)
2/5
(c)
3/5
(d)
13/30

Answer: Option D

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Explanation :

P (problem is solved) = P (only A solves) + P (only B solves) + P (only C solves).

∴ P (only A solves) = P (A solves) × P (B doesn’t solve) × P (C doesn’t solves)

∴ P (only A solves) = $\frac{1}{3} \times \frac{3}{4} \times \frac{4}{5}$ = $\frac{1}{5}$

Similarly, P (only B solves) = $\frac{2}{3} \times \frac{1}{4} \times \frac{4}{5}$ = $\frac{2}{15}$

Similarly, P (only C solves) = $\frac{2}{3} \times \frac{3}{4} \times \frac{1}{5}$ = $\frac{1}{10}$

∴ P (problem is solved) = $\frac{1}{5} + \frac{2}{15} + \frac{1}{10}$ = $\frac{6 + 4 + 3}{30}$ = $\frac{13}{30}$ .

Hence, option (d).

10. CRE 1 - Basics | Modern Math - Probability

Find the probability that at least one of them will solve it.

(a)
1/60
(b)
2/5
(c)
3/5
(d)
13/30

CRE 1 - Basics | Modern Math - Probability

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