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In a town 45% people speak English, 30% speak Hindi and 20% speak both English and Hindi. One person is selected at random. Find the probability that he speaks English, if it is known that he speaks Hindi.

A.

1/3

B.

2/3

C.

5/6

D.

2/5

Answer with explanation

Answer: Option BExplanation

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There are 8 brown balls, 4 orange balls and 5 black balls in a bag. Five balls are chosen at random. What is the probability of their being 2 brown balls, 1 orange ball and 2 black balls ?

A.

191/1547

B.

180/1547

C.

280/1547

D.

189/1547

Answer with explanation

Answer: Option CExplanation

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When 4 fair coins are tossed together what is the probability of getting at least 3 heads?

A.

1/4

B.

3/4

C.

5/16

D.

3/8

Answer with explanation

Answer: Option CExplanation

When 4 fair coins are tossed simultaneously, the total number of outcomes is 2^{4} = 16

At least 3 heads implies that one can get either 3 heads or 4 heads.

One can get 3 heads in ^{4}C_{3} = 4 ways and can get 4 heads in ^{4}C_{4} = 1 ways.

∴ Total number of favorable outcomes = 4 + 1 = 5

====>>> The required probability = 1/4.

or

The answer is 5/16 because in total there are 16 possibilities when tossing a coin 4 times. I.e. 2⋅2⋅2⋅2=242⋅2⋅2⋅2=24.

And the possibilities of getting atleast three head is 5 that is we can get HHHT, HHTH, HTHH, THHH, and HHHH

Thus, the answer is 5/16.

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A basket contains 10 apples and 20 oranges out of which 3 apples and 5 oranges are defective. If we choose two fruits at random, what is the probability that either both are oranges or both are non defective?

A.

158/435

B.

316/435

C.

17/87

D.

136/345

Answer with explanation

Answer: Option BExplanation

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Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even ?

A.

1/4

B.

1/2

C.

3/4

D.

7/4

Answer with explanation

Answer: Option CExplanation

Total number of cases = 6*6 = 36

Favourable cases = [(1,2),(1,4),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,2),(3,4),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,2),(5,4),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)] = 27

So Probability = 27/36 = 3/4

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Two unbiased coins are tossed. What is the probability of getting at most one tail?

A.

3/4

B.

1/2

C.

3/2

D.

1/4

Answer with explanation

Answer: Option AExplanation

Total 4 cases = [HH, TT, TH, HT]

Favourable cases = [HH, TH, HT]

Please note we need atmost one tail, not atleast one tail.

So probability = 3/4

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A pot contains 5 white and 3 red balls while another pot contains 4 white and 6 red balls. One pot is chosen at random and a ball is drawn from it. If the ball is white, what is the probability that it is from the first pot?

A.

1/5

B.

5/16

C.

25/41

D.

41/80

Answer with explanation

Answer: Option CExplanation

The probability of choosing one pot = 1/2

The probability of choosing white ball in first pot = 1/2 × [ 5C1 / 8C1] = 5/16

The probability of choosing white ball

= 1/2 × [5C1 / 8C1] + 1/2 × [4C1 / 10C1]

= 1/2 × [5/8] + 1/2 × [4/10]

= 5/16 + 1/5 = 41/80 ∴ The probability that it is from the first pot = (5/16) / (41/80)

= 5/16 × 80/41 = 25/41

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In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?

A.

16/21

B.

9/14

C.

5/21

D.

5/14

Answer with explanation

Answer: Option CExplanation

Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)

As remaining person can be any one among three couples left.

Required probability = (⁵C₂ * ⁶C₁)/¹⁰C₅ ==>> (10 * 6)/252 = 5/21

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A man and his wife appear in an interview for two vacancies in the same post. The probability of husband’s selection is (1/7) and the probability of wife’s selection is (1/5). What is the probability that only one of them is selected ?

A.

3/4

B.

2/7

C.

4/5

D.

1/7

Answer with explanation

Answer: Option BExplanation

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A dice is thrown, what is the probability that the number obtained is a prime number.

A.

1/3

B.

1/6

C.

1/8

D.

1/2

Answer with explanation

Answer: Option DExplanation

Dice is thrown, the total possible outcomes = 6.

Favorable outcomes = 3 i.e. (2,3,5). Probability = 3 / 6 = 1 / 2

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