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
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
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
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
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
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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