Test: Probability- 1

QUESTION: 1

A die is rolled twice. What is the probability of getting a sum equal to 9?

A.
B.
C.
D.

Solution:

► Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)

Hence, total number of outcomes possible when a die is rolled twice, n(S) = 6 x 6 = 36

► E = Getting a sum of 9 when the two dice fall = {(3,6), (4,5), (5,4), (6,3)}

Hence, n(E) = 4

QUESTION: 2

A bag contains 2 yellow, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

A.
B.
C.
D.

Solution:

Total number of balls = 2 + 3 + 2 = 7

► Let S be the sample space.

n(S) = Total number of ways of drawing 2 balls out of 7 = ⁷C₂

► Let E = Event of drawing 2 balls, none of them is blue.

n(E) = Number of ways of drawing 2 balls from the total 5 (= 7-2) balls = ⁵C₂
(∵ There are two blue balls in the total 7 balls. Total number of non-blue balls = 7 - 2 = 5)

QUESTION: 3

Three coins are tossed. What is the probability of getting at most two tails?

A.
B.
C.
D.

Solution:

► Total number of outcomes possible when a coin is tossed = 2 (∵ Head or Tail)

Hence, total number of outcomes possible when 3 coins are tossed, n(S) = 2 x 2 x 2 = 8
(∵ S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH})

► E = event of getting at most two Tails = {TTH, THT, HTT, THH, HTH, HHT, HHH}

Hence, n(E) = 7

QUESTION: 4

When tossing two coins once, what is the probability of heads on both the coins?

A.
B.
C.
D.
None of these

Solution:

► Total number of outcomes possible when a coin is tossed = 2 (∵ Head or Tail)

Hence, total number of outcomes possible when two coins are tossed, n(S) = 2 x 2 = 4
(∵ Here, S = {HH,HT,TH,TT})

► E = event of getting heads on both the coins = {HH}

Hence, n(E) = 1

QUESTION: 5

What is the probability of getting a number less than 4 when a die is rolled?

A.
B.
C.
D.

Solution:

Total number of outcomes possible when a die is rolled = 6
(∵ any one face out of the 6 faces) i.e., n(S) = 6
E = Getting a number less than 4 = {1, 2, 3}
Hence, n(E) = 3

QUESTION: 6

A bag contains 4 black, 5 yellow and 6 green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow?

A.
B.
C.
D.

Solution:

Total number of balls = 4 + 5 + 6 = 15

► Let S be the sample space.

n(S) = Total number of ways of drawing 3 balls out of 15 = ¹⁵C₃

► Let E = Event of drawing 3 balls, all of them are yellow.

n(E) = Number of ways of drawing 3 balls from the total 5 = ⁵C₃
(∵ there are 5 yellow balls in the total balls)

[∵ ⁿC_r = ⁿC₍_n-r). So ⁵C₃ = ⁵C₂. Applying this for the ease of calculation]

QUESTION: 7

One card is randomly drawn from a pack of 52 cards. What is the probability that the card drawn is a face card(Jack, Queen or King)

A.
B.
C.
D.

Solution:

Total number of cards, n(S) = 52
Total number of face cards, n(E) = 12 (4 Jacks, 4 Queens, 4 Kings)

QUESTION: 8

A dice is thrown. What is the probability that the number shown in the dice is divisible by 3?

A.
B.
C.
D.

Solution:

Total number of outcomes possible when a die is rolled, n(S) = 6 (? 1 or 2 or 3 or 4 or 5 or 6)
E = Event that the number shown in the dice is divisible by 3 = {3, 6}
Hence, n(E) = 2