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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.

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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.

In first bag. there are 4 red and 5 black balls and in second bag, there are 3 red and 7 black balls.
P(two red and one black ball) = P(‘one red ball from first bag and one red, one black from second bag’ or ‘one black ball from first bag and two red balls from second bag’ )
= P(one red ball from first bag and one red. one black from second bag) + P(one black ball from first bag and two red balls from second bag).

$equals space 4 over 9 cross times fraction numerator straight C presuperscript 3 subscript 1 cross times straight C presuperscript 7 subscript 1 over denominator straight C presuperscript 10 subscript 2 end fraction plus 5 over 9 cross times fraction numerator straight C presuperscript 3 subscript 2 over denominator straight C presuperscript 10 subscript 2 end fraction space equals 4 over 9 cross times fraction numerator begin display style 3 over 1 end style cross times begin display style 7 over 1 end style over denominator begin display style fraction numerator 10 cross times 9 over denominator 1 cross times 2 end fraction end style end fraction plus 5 over 9 cross times fraction numerator begin display style fraction numerator 3 cross times 2 over denominator 1 cross times 2 end fraction end style over denominator begin display style fraction numerator 10 cross times 9 over denominator 1 cross times 2 end fraction end style end fraction equals space 4 over 9 cross times 7 over 15 plus 5 over 9 cross times 1 over 15 space equals 28 over 135 plus 5 over 135 space equals space 33 over 135 space equals space 11 over 45$

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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