Probability
Direction: Study the following information carefully to answer the question the question that follow.
A box contains 2 blue caps, 4 red caps, 5 green caps and 1 yellow cap.
- If two caps are picked at random, what is the probability that atleast one is red ?
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Required probability = 1 - 8C2/ 12C2
Correct Option: C
Required probability = 1 - 8C2/ 12C2
= 1 - 28/66 = 38/66 = 19/33
Direction: Study the given information carefully and answer the questions that follow.
A basket contains 4 red, 5 blue and 3 green marbles.
- If two marbles are drawn at random, what is the probability that both are red ?
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Total number of possible outcomes
= n(S) = 12C2 = (12 x 11)/2 = 66
Total number of favorable events
= n(E) = 4C2
= (4 x 3) / (2 x 1) = 6Correct Option: D
Total number of possible outcomes
= n(S) = 12C2 = (12 x 11)/2 = 66
Total number of favorable events
= n(E) = 4C2
= (4 x 3) / (2 x 1) = 6
∴ Required probability = 6/66 = 1/11
- Four boys and three girl stand in queue for an interview. The probability that they stand in alternate position is
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Total number of possible arrangement for 4 boy and 3 girls in a queue = 7!
when they occupy alternate position then the arrangement would be like
BGBGBGB. Thus the total number of possible arrangement = 4! x 3!Correct Option: B
Total number of possible arrangement for 4 boy and 3 girls in a queue = 7!
when they occupy alternate position then the arrangement would be like
BGBGBGB. Thus the total number of possible arrangement = 4! x 3!
∴ Required probability = 4! x 3! / 7!
= (4 x 3 x 2 x 3 x 2) / (7 x 6 x 5 x 4 x 3 x 2) = 1/35
- An anti-aircraft gun can take a maximum of four shots at an enemy plane moving away from it ,The probability of hitting the plane at the first, second, third and fourth shots are 0.4, 0.3, 0.2, and 0.1 respectively. What is the probability that the plane is hit when all the four shots are fired?
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First we find the probability that the plane is not hit
= (1 - 0.4) ( 1 - 0.3) (1 - 0.2) (1 - 0.1)
= 0.6 x 0.7 x 0.8 x 0.9 = 0.3024Correct Option: C
First we find the probability that the plane is not hit
= (1 - 0.4) ( 1 - 0.3) (1 - 0.2) (1 - 0.1)
= 0.6 x 0.7 x 0.8 x 0.9 = 0.3024
∴ probability that the plane is hit = 1 - 0.3024
= 0.6976
- Murari has 9 pair of dark blue socks and 9 pair of black socks. He keeps them all in the same bag. If he picks out three socks at random What is the probability that he will get a matching pair?
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Since, there are only two types of socks in the bag. so, if murari pick up 3 socks then certainly two of them are of same type. Thus this is a certain event.
Correct Option: C
Since, there are only two types of socks in the bag. so, if murari pick up 3 socks then certainly two of them are of same type. Thus this is a certain event.
Hence required probability = 1
