Direction: Study the given information carefully and answer the questions that follow—

A store contains 4 red, 5 blue, 4 green shirts.

If two shirts are picked at random, what is the probability that both are green?

Probabilities if both are green

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Direction: Study the following information carefully and answer the questions that follow:

A committee of five members is to be formed out of 3 trainees, 4 professors and 6 engineers.

In how many ways this can be done if at least 3 trainees to have to be included in a committee

Number of Ways when if at least 3 trainees include in committee =

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

A store contains 5 red, 4 blue, 5 green shirts.

If two shirts are picked at random, what is the probability that both are blue?

Probabilities if both are blue

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In a basket there are 7 apples and 8 oranges. 4 fruits are picked at random. What is the probability that two fruits are apples and 2 are oranges?

**A. ** 72/455

**B. ** 82/455

**C. ** 89/455

**D. ** 84/455

**E. ** None of these

**Answer : ****Option E**

**Explaination / Solution: **

Total number of fruits n(s) =7 + 8=15

Probability = (^{7}C_{2}*^{8}C_{2})/^{15}C_{4}

= (21*28)/1365 = 28/65

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If four bats are picked at random, what is the probability that two are blue and two is green?

**A. ** 12/455

**B. ** 35/355

**C. ** 18/455

**D. ** 18/35

**E. ** None of these

**Answer : ****Option A**

**Explaination / Solution: **

Probability if two are Blue and two are Green =

[(^{4}C_{2}*^{4}C_{2})/^{15}C_{4}] = (6*6)/1365 → 12/455

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Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.

**A. ** 0.2

**B. ** 1

**C. ** 0

**D. ** 0.5

**Answer : ****Option C**

**Explaination / Solution: **

S = {(3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6), (1,H), (2,H), (4,H), (5,H), (1,T), (2,T), (4,T), (5,T)} Let A = event that coin shows a tail. i.e. A = { (1,T), (2,T), (4,T), (5,T)} and B = event that atleast one die shows 3. B = {(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),(6,3)}

S = {(3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6), (1,H), (2,H), (4,H), (5,H), (1,T), (2,T), (4,T), (5,T)} Let A = event that coin shows a tail. i.e. A = { (1,T), (2,T), (4,T), (5,T)} and B = event that atleast one die shows 3. B = {(3,1), (3,2), (3,3), (3,4), (3,5), (3,6),(6,3)}

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The conditional probability of an event E, given the occurrence of the event F lies between

**A. ** 0 < P (E|F) ≤ 1

**B. ** 0 < P (E|F) < 1

**C. ** 0 ≤ P (E|F) ≤ 1

**D. ** 0 ≤ P (E|F) < 1

**Answer : ****Option C**

**Explaination / Solution: **

As the probability of any event always lies between 0 and 1. Therefore , 0 ≤ P (E|F) ≤ 1.

As the probability of any event always lies between 0 and 1. Therefore , 0 ≤ P (E|F) ≤ 1.

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If P (A) = 0.8, P (B) = 0.5 and P(B|A) = 0.4, find P(A ∪ B)

**A. ** 0.98

**B. ** 1.00

**C. ** 0.95

**D. ** 0.25

**Answer : ****Option A**

**Explaination / Solution: **

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A pair of dice is tossed once and a total of 8 has come up. The chance that both the dice show up same number is

**A. ** 5/ 216

**B. ** none of these

**C. ** 1/ 5

**D. ** 1/ 6

**Answer : ****Option C**

**Explaination / Solution: **

on tossing a pair of dice total outcomes are 36

out of which getting a total of 8 have possiblities {(2,6),(6,2),(3,5),(5,3),(4,4)}=5

and from these 5 outcomes getting same no. on both dice is (4,4)=1

so, probability is 1/5

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8 coins are tossed at a time. The probability of getting atleast 6 heads up is

**A. ** 1/ 64

**B. ** 229/ 256

**C. ** 57/ 64

**D. ** 37/ 256

**Answer : ****Option D**

**Explaination / Solution: **

No Explaination.

No Explaination.

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