Probability Quiz for RBI 2 marks

1. 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. 1/2	B. 10/21
C. 9/11	D. 7/11

Answer : Option B

Explanation :

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 , none of them is blue
= 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)

P(E) = n(E)n(S)=5C27C2=(5×42×1)(7×62×1)=5×47×6=1021

2. A die is rolled twice. What is the probability of getting a sum equal to 9?
A. 23	B. 29
C. 13	D. 19

Answer : Option D

Explanation :

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 × 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

P(E) = n(E)n(S)=436=19

3. Three coins are tossed. What is the probability of getting at most two tails?
A. 78	B. 18
C. 12	D. 17

Answer : Option A

Explanation :

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Solution 1
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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 × 2 × 2 = 8

(∵ i.e., 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

P(E) = n(E)n(S)=78

4. When tossing two coins once, what is the probability of heads on both the coins?
A. 14	B. 12
C. 34	D. None of these

Answer : Option A

Explanation :

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Solution 1
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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 × 2 = 4

(∵ Here, S = {HH, HT, TH, TT})

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

Hence, n(E) = 1

P(E) = n(E)n(S)=14

5. What is the probability of getting a number less than 4 when a die is rolled?
A. 12	B. 16
C. 13	D. 14

Answer : Option A

Explanation :

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

P(E) = n(E)n(S)=36=12

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. 291	B. 181
C. 18	D. 281

Answer : Option A

Explanation :

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, all of them are yellow
= Number of ways of drawing 3 balls from the total 5 = ⁵C₃
(∵ there are 5 yellow balls in the total balls)

P(E) = n(E)n(S)

=5C315C3=5C215C3 [∵ ⁿC_r = ⁿC_{(n - r)}. So ⁵C₃ = ⁵C₂. Applying this for the ease of calculation]

=(5×42×1)(15×14×133×2×1)=5×4(15×14×133)=5×45×14×13=414×13=27×13=291