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Dell Probability Questions

June 23, 2019

Question 1

Time: 00:00:00

A bag contains 6 white and 4 black balls .2 balls are drawn at random. 

Find the probability that they are of same colour.

1/2

1/2

7/5

7/5

8/15

8/15

1/9

1/9

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PrepInsta Explanation
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Let S be the sample space
Then n(S) = no of ways of drawing 2 balls out of (6+4)
=10C2 10 =10*9/2*1 =45

Let E = event of getting both balls of same colour

Then,n(E) = no of ways (2 balls out of six) or
(2 balls out of 4)

=6C2+4C2 = 6*5/2*1+4*3/2*1
= 15+6 = 21
Therefore, P(E) = n(E)/n(S) = 21/45 = 7/15

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Question 2

Time: 00:00:00

Tickets numbered 1 to 20 are mixed up and then a ticket is 

drawn at random. What is the probability that the ticket 

drawn has a number which is a multiple of 3 or 5?

1/2

1/2

3/5

3/5

9/20

9/20

8/15

8/15

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Here, S = {1, 2, 3, 4, ...., 19, 20}.

Let E = event of getting a multiple of 3 or 5 =
{3, 6 , 9, 12, 15, 18, 5, 10, 20}.

P(E) = n(E)/n(S) = 9/20.

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Question 3

Time: 00:00:00

Two dice are tossed. The probability that the total score is 

a prime number is:

5/2

5/2

1/6

1/6

1/2

1/2

7/9

7/9

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Clearly, n(S) = (6 x 6) = 36.

Let E = Event that the sum is a prime number.

Then E= { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5),
(3, 2), (3, 4), (4, 1), (4,3),(5, 2), (5, 6), (6, 1), (6, 5) }

n(E) = 15.

P(E) = n(E)/n(S) = 15/36 = 5/12.

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Question 4

Time: 00:00:00

A bag contains 4 white, 5 red and 6 blue balls. Three balls 

are drawn at random from the bag. The probability that all 

of them are red, is:

2/91

2/91

1/22

1/22

3/22

3/22

2/77

2/77

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Then, n(S) = number of ways of drawing 3 balls out of 15
= 15C3 =(15*14*13)/(3*2*1)= 455.

Let E = event of getting all the 3 red balls.

n(E) = 5C3 = 5*4/2*1 = 10.

=> P(E) = n(E)/n(S) = 10/455 = 2/91.

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Question 5

Time: 00:00:00

In a lottery, there are 10 prizes and 25 blanks. A lottery is 

drawn at random. What is the probability of getting a prize?

2/7

2/7

5/7

5/7

1/5

1/5

1/2

1/2

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Total number of outcomes possible, n(S)
= 10 + 25 = 35

Total number of prizes, n(E) = 10

P(E)=n(E)/n(S)=10/35=2/7

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Question 6

Time: 00:00:00

What is the probability of getting 53 Mondays in a leap year?

1/7

1/7

3/7

3/7

2/7

2/7

1

1

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1 year = 365 days . A leap year has 366 days

A year has 52 weeks.
Hence there will be 52 Sundays for sure.

52 weeks = 52 x 7 = 364days

366 – 364 = 2 days

In a leap year there will be 52 Sundays and
2 days will be left.

These 2 days can be:

1. Sunday, Monday

2. Monday, Tuesday

3. Tuesday, Wednesday

4. Wednesday, Thursday

5. Thursday, Friday

6. Friday, Saturday

7. Saturday, Sunday

Of these total 7 outcomes,
the favourable outcomes are 2.

Hence the probability of getting 53 days = 2/7

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Question 7

Time: 00:00:00

One card is drawn at random from a pack of 52 cards. 

What is the probability that the card drawn is a face card 

(Jack, Queen and King only)?

3/13

3/13

1/13

1/13

3/52

3/52

9/52

9/52

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Clearly, there are 52 cards,
out of which there are 12 face cards.

P (getting a face card) = 12/52=3/13.

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Question 8

Time: 00:00:00

Two cards are drawn together from a pack of 52 cards. 

The probability that one is a spade and one is a heart, is:

3/20

3/20

29/34

29/34

47/100

47/100

13/102

13/102

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PrepInsta Explanation
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Let S be the sample space.
Then, n(S) = 52C2=(52 x 51)/(2 x 1) = 1326.
Let E = event of getting 1 spade and 1 heart.
n(E)= number of ways of choosing 1 spade out
of 13 and 1 heart out of 13 = 13C1*13C1 = 169.
P(E) = n(E)/n(S) = 169/1326 = 13/102.

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Question 9

Time: 00:00:00



A bag contains 6 black and 8 white balls. One ball is drawn 

at random. What is the probability that the ball drawn is white?

3/7

3/7

4/7

4/7

1/8

1/8

3/4

3/4

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Let number of balls = (6 + 8) = 14.

Number of white balls = 8.

P (drawing a white ball) = 8 /14 = 4/7.

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Question 10

Time: 00:00:00



If two letters are taken at random from the word HOME, 

what is the probability that none of the letters would be vowels?

1/6

1/6

1/2

1/2

1/3

1/3

1/4

1/4

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P(first letter is not vowel) = 24

P(second letter is not vowel) = 1/3

So, probability that none of letters would be
vowels is = 2/4×1/3=1/6

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["0","40","60","80","100"]

["Need more practice! \n","Keep trying! \n","Not bad! \n","Good work! \n","Perfect! \n"]

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One comment on “Dell Probability Questions”

Rahul Sahani
please provide the solution to the above questions

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