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Probability questions and answer

1)A carry bag contains 5 white, 8 violet and 3 pink ribbons. Four ribbons are drawn at random. What is the probability that none of the ribbons drawn is pink?
A. 10/20
B. 11/20
C. 2/7
D. 5/7

Answer:B. 11/20

Explanation: Total number of ribbons = (5 + 8 + 3) = 16
Let S be the sample.
Then, n(S)= Number of ways of drawing 4 ribbons out of 16
= 16C4`
=(16 x 15)/(4 x 3)
= 20.
Let E = Event of drawing 4 ribbons, none of which is pink.
n(E) = Number of ways of drawing 4 balls out of (12) ribbons.
= 12C4
= (12 x 11)/(4 x 3)
= 11.
P(E) = n(E)/n(S)
=11/20

2) What is the probability of getting a sum 9 from two throws of a dice?
A. 1/5
B. 1/8
C. 1/7
D. 1/9

Answer:D. 1/9

Explanation: In two throws of a dice, n(S) = (6 x 6) = 36.
Let E = event of getting a sum
={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E) = n(E)/n(S)
=4/36
=1/9

3) In a box, there are 4 green, 3 brown and 7 red balls. One ball is picked up randomly. What is the probability that it is neither green nor red?
A. 3/14
B. 3/4
C. 7/19
D. 8/21

Answer:A. 3/14

Explanation: Total number of balls = (4 + 3 + 7) = 14.
Let E = event that the ball drawn is neither red nor green
= event that the ball drawn is brown.
n(E) = 3.
P(E) = n(E)/n(S)
=3/14

4) What is the probability that a number selected from numbers 1,2,3,...,25, is prime number, when each of the given numbers is equally likely to be selected?
A. 9/30
B. 8/30
C. 9/30
D. 11/30

Answer: C. 9/30

Explanation: Total prime no= {2,3,5,7,11,13,17,19,23}
n(E)= 9
n(S)=30
Hence required probability,
P(E) = n(E)/n(S)
=9/30

5)A bag contains 20 toys numbered 1 to 20. A toy is drawn and then another toy is drawn without replacement. Find the probability that both toys will show even numbers.
A. 5/21
B. 9/38
C. 11/42
D. 4/21

Answer:B. 9/38

Explanation: The probability that first toy shows the even number,
= 10/20
Since, the toy is not replaced there are now 9 even numbered toys and total 19 toys left.
Hence, probability that second toy shows the even number,
= 9/19
Required probability,
P(E) = 10/20 × 9/19
=9/38






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