Examples(Set 3) - Probability

11. 4 coins are tossed together. What is the probability of getting exactly 2 heads ?
A. 1/4
B. 1/ 3
C. 3/8
D. 1/ 8

Answer: Option C

Total number of outcomes possible when a coin is tossed = 2 (∵ Head or Tail)
Hence, total number of outcomes possible when 4 coins are tossed, n(S)
=24
n(E) = Number of ways of getting exactly 2 heads when 4 coins are tossed
= 4 C 2
P(E) = n(E)/ n(S)

= 4 C 2
  24

= 3/8






12.What is the probability of drawing a "King" from a deck of 52 cards?
A. None of these
B. 1/ 4
C. 1/ 2
D. 3/ 4

Answer: Option B

Explanation:
Total number of cards, n(S) = 52
Total number of 'King" cards, n(E) = 4
P(E) = n(E)/ n(S)
= 4/ 52
= 1/ 4






13. What is the probability of selecting a prime number from 1 , 2 , 3 , ⋯ 15 ?
A. 7/15
B. 6/14
C. 1/3
D. 6/15

Answer: Option D

Explanation:
Total count of numbers, n(S) = 15
Prime numbers in the given range are { 2 , 3 , 5 , 7, 11, 13}
n(E) = 6
P(E) = n(E)/ n(S)
= 6/ 15






13.One card is randomly drawn from a pack of 52 cards. What is the probability that the card drawn is a daimond card
A. 1/ 4
B. 1/2
C. 1/3
D. 1/8

Answer: Option A

Explanation:
Total number of cards, n(S) = 52
Total number of daimond cards, n(E) = 13
P(E) = n(E)/ n(S)
= 13/ 52
= 1/4






15. 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. 2/ 81
B. 2/ 91
C. 1/ 81
D. 1/ 8

Answer: Option B

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
= 15 C 3
n(E) = Number of ways of drawing 3 balls from the total 5
= 5 C 3
P(E) = n(E)/ n(S)
=(5 C 3 )
 15 C 3
= (5 x 4 x 3/ 3 x 2x 1)   
( 15 × 14 × 13/ 3 × 2 × 1 )
= 2/ 91






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