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Probability

Short Answer Type

851. An urn contains 6 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting 2 red balls.

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852. An urn contains 6 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting 2 blue balls.

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853. An urn contains 6 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting one red and one blue ball.

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854. Three groups of children contain respectively 3 girls and 1 boy; 2 girls and 2 boys; 1 girl and 2 boys. One child is selected at random from each group. Show that the probability that the three selected consist of 1 girl and 2 boys is $3 over 8.$

Group I Group II Group III
Boys 1 2 2
Girls 3 2 1
P (1 girl and two boys) = P(GBB) + P(BGB) + P(BBG)
= P(G) P(B) P(B)+ P(B) P(G) P(B) + P(B) P(B) P(G)

$equals space 3 over 4 cross times 2 over 4 cross times 2 over 3 plus 1 fourth cross times 2 over 4 plus 2 over 3 cross times 1 fourth cross times 2 over 4 cross times 1 third space equals space 12 over 48 plus 4 over 48 plus 2 over 48 space equals space 18 over 48 space equals space 3 over 8$

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855. A bag contains 5 white and 3 black balls. Four balls are drawn one at a time without replacement. Find the probability that the ball are alternatively of different colours.

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856. A bag contains 3 red and 5 black balls and second bag contains 6 red and 4 black balls. A ball is drawn from each bag. Find the probability that one is red and other is black.

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857. A bag contains 4 white and 2 black balls, and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, find the probability that one is white and the other black.

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858. A bag has 4 red and 5 black balls, a second bag has 3 red and 7 black balls. One ball is drawn from the first and two from the second. Find the probability that out of three balls two are red and one is black.

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859.

Fatima and John appear in an interview for two vacancies in the same post. The probability of Fatima's selection is $1 over 7 space and space$ that of John's selection is $1 fifth.$ what is the probability that both of them will be selected?

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860.

Fatima and John appear in an interview for two vacancies in the same post. The probability of Fatima's selection is $1 over 7 space and space$ that of John's selection is $1 fifth.$ What is the probability that only one of them is selected?

82 Views