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

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