## AMCAT PREVIOUS PLACEMENT PAPER QUESTIONS-9

Ques. A box contains 4 red, 3 white and 2 blue balls. Three balls are drawn at random. Find out the number of ways of selecting the balls of different colours

12

24

48

168

Explanation:

This question seems to be a bit typical, isn’t, but it is simplest.

1 red ball can be selected in 4C1 ways

1 white ball can be selected in 3C1 ways

1 blue ball can be selected in 2C1 ways

Total number of ways

= 4C1 x 3C1 x 2C1

= 4 x 3 x 2

= 24

Please note that we have multiplied the combination results, we use to add when their is OR condition, and we use to multiply when there is AND condition, In this question it is AND as

1 red AND 1 White AND 1 Blue, so we multiplied.

Three unbiased coins are tossed, what is the probability of getting at least 2 tails ?

1/3

1/6

1/2

1/8

Explanation:

Total cases are = 2*2*2 = 8, which are as follows

[TTT, HHH, TTH, THT, HTT, THH, HTH, HHT]

Favoured cases are = [TTH, THT, HTT, TTT] = 4

So required probability = 4/8 = ½

Ques. In a throw of dice what is the probability of getting number greater than 5

1/2

1/3

1/5

1/6

Explanation:

Number greater than 5 is 6, so only 1 number

Total cases of dice = [1,2,3,4,5,6]

So probability = ⅙

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

3/4

1/4

7/4

1/2

Explanation:

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 = ¾

Ques. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor green?

2/3

8/21

3/7

9/22

Explanation:

Total number of balls = (8 + 7 + 6) = 21

Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red.

Therefore, n(E) = 8.

P(E) = 8/21.

Ques. A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is

1/13

2/13

1/26

1/52

Explanation:

Total number of cases = 52

Favourable cases = 2

Probability = 2/56 = 1/26

Ques. A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident

30%

35%

40%

45%

Explanation:

Let A = Event that A speaks the truth

B = Event that B speaks the truth

Then P(A) = 75/100 = 3/4

P(B) = 80/100 = 4/5

P(A-lie) = 1-3/4 = 1/4

P(B-lie) = 1-4/5 = 1/5

Now

A and B contradict each other =

[A lies and B true] or [B true and B lies]

= P(A).P(B-lie) + P(A-lie).P(B)

= (3/5*1/5) + (1/4*4/5) = 7/20

= (7/20 * 100) % = 35%

Ques. From a pack of 52 cards, two cards are drawn together, what is the probability that both the cards are kings

2/121

2/221

1/221

1/13