# CRE 1 - Basics | Modern Math - Probability

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**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

Answer: Option A

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**Explanation** :

Total numbers of letters in the work ELEPHANT is 8.

Number of vowels is 3 (i.e., 1 A and 2 Es)

∴ Probability of selecting a vowel = 3/8.

Hence, option (a).

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**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

Answer: Option C

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**Explanation** :

Number or perfect squares in first 100 natural numbers is 10 (1^{2}, 2^{2}, …, 10^{2}).

∴ Probability of selecting a perfect square = 10/100 = 1/10.

Hence, option (c).

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**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 = ^{10}C_{3}

Number of ways of choosing defected bulbs = ^{4}C_{3}

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

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

Hence, option (b).

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**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

Answer: Option D

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**Explanation** :

Odds in favor of man = 1 : 2

∴ P (man is selected) = 1/3

Similarly, P (woman is selected) = 3/4

P (neither man nor woman is selected) = P (man is not selected) × P (woman is not selected)

∴ Required probability = 2/3 × 1/4 = 1/6

Hence, option (d).

Workspace:

**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: Option C

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**Explanation** :

Number of multiples of 5 between 1 and 75 = 15

Number of multiples of 7 between 1 and 75 = 10

Number of multiples of 35 between 1 and 75 = 2

∴ Number of multiples of 5 or 7 between 1 and 75 = 15 + 10 – 2 = 23.

∴ Required probability = 23/75

Hence, option (c).

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**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 $\frac{1}{5}$.

**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) = $\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)$ = $\frac{2}{3}\times \frac{3}{4}\times \frac{4}{5}$ = $\frac{2}{5}$

Hence, option (b).

Workspace:

**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) = $\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)$ = $\frac{2}{3}\times \frac{3}{4}\times \frac{4}{5}$ = $\frac{2}{5}$

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

Hence, option (c).

Workspace:

**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

Answer: Option C

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**Explanation** :

Consider the solution to seventh question of this exercise.

P (problem is solved) = P (at least one of them solves it) = 3/5

Hence, option (c).

Workspace:

**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).

Workspace:

**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

Answer: Option C

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**Explanation** :

Consider the solution to seventh question of this exercise.

P (problem is solved) = P (at least one of them solves it) = 3/5

Hence, option (c).

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