AMCAT Quantitative Ability Previous Question Papers with solutions-1

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
Answer And Explanation
Answer: Option A

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

Answer: Option B

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
Answer And Explanation
Answer: Option C

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%
Answer And Explanation
Answer: Option B

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)
[Please note that we are adding at the place of OR]
= (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
Answer And Explanation
Answer: Option C

Explanation:

Total cases =52C2=52∗51/2∗1=1326
Total King cases =4C2=4∗3/2∗1=6
Probability ==6/1326=1/221

Ques. A box contains 5 green, 4 yellow and 3 white balls. Three balls are drawn at random. What is the probability that they are not of same colour.
52/55
3/55
41/44
3/44

Ques. Bag contain 10 back and 20 white balls, One ball is drawn at random. What is the probability that ball is white
1
2/3
1/3
4/3
Answer And Explanation
Answer: Option B

Explanation:

Total cases = 10 + 20 = 30
Favourable cases = 20

So probability = 20/30 = ⅔

There is a pack of 52 cards and Rohan draws two cards together, what is the probability that one is spade and one is heart ?
11/102
13/102
11/104
11/102
Answer And Explanation
Answer: Option B

Explanation:

Two cards are drawn together from a pack of 52 cards. The probability that one is a spade and one is a heart, is:

Let sample space be S