Examples(Set 2) - Probability

6. A dice is thrown. What is the probability that the number shown in the dice is divisible by 2 ?
A. 1/ 6
B. 1/ 3
C. 1/ 2
D. 1/ 4

Answer: Option C

Explanation:
The possible outcomes when a die thrown is {1,2,3,4,5,6}.
Therefore, the number of possible outcomes of a die is 6.
i.e., n(S) = 6
E = Event that the number shown in the dice is divisible by 2
= {2,4,6}
n(E) = 3
P(E) = n(E)/ n(S)
= 3/ 6
= 1/ 2






7.Doramon draws a card from a pack of cards. What is the probability that the card drawn is a card of red suit?
A. None of these
B. 1/ 4
C. 1/ 2
D. 3/ 4

Answer: Option C

Explanation:
Total number of cards, n(S) = 52
Total number of red cards, n(E) = 26
P(E) = n(E)/ n(S)
= 26/ 52
= 1/ 2






8. There are 15 boys and 10 girls in a class. If three students are selected at random, what is the probability that 1 girl and 2 boys are selected?
A. 21/ 46
B. 1/ 2
C. 1/ 40
D. 7/ 42

Answer: Option A

Explanation:
n(S) = Total number of ways of selecting 3 students from 25 students
= 25 C 3
n(E) = Number of ways of selecting 1 girl and 2 boys from 10 girls and 15 boys
n(E) = 15 C 2 × 10 C 1
P(E) = n(E)/ n(S)
= (15C2 × 10C1)
         25 C 3
= 21/ 46






9.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. 1/ 13
B. 3/ 13
C. 4/ 13
D. 2/ 13

Answer: Option B

Explanation:
Total number of cards, n(S) = 52
Total number of face cards, n(E) = 12
P(E) = n(E)/ n(S)
= 12/ 52
= 3/ 13






10. 3 balls are drawn randomly from a bag contains 3 black, 5 red and 4 blue balls. What is the probability that the balls drawn contain balls of different colors?
A. 3/ 11
B. 1/ 3
C. 1/ 2
D. 2/ 11

Answer: Option A

Explanation:
Total number of balls
=3 + 5 + 4 = 12
Let S be the sample space.
n(S) =Total number of ways of drawing 3 balls out of 12 = 12 C 3
n(E) =drawing 3 different coloured balls.
=one black ball from 3 black balls, one red ball from 5 red balls, one blue ball from 4 blue balls.
= 3 C 1 × 5 C 1 × 4 C 1
P(E) = n(E)/ n(S)
=(3 C 1 × 5 C 1 × 4 C 1)
 12 C 3
= 3 × 5 × 4  
( 12 × 11 × 10 /3 × 2 × 1 )
= 3/ 11






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