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
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
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
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
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
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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