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Probability

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by vaibhav101 » Sat Jun 16, 2018 1:26 am

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a box contains 2 tennis, 3 cricket and 4 squash balls. 3 balls are drawn in succession with replacement. Find the probability that all 3 are of same type.

A 12/81
B 1/9
C 18/81
D 11/81
E none of these
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by Brent@GMATPrepNow » Sat Jun 16, 2018 4:34 am
vaibhav101 wrote:a box contains 2 tennis, 3 cricket and 4 squash balls. 3 balls are drawn in succession with replacement. Find the probability that all 3 are of same type.

A 12/81
B 1/9
C 18/81
D 11/81
E none of these
P(all 3 are same type) = P(all 3 are tennis OR all 3 are cricket OR all 3 are squash)
= P(all 3 are tennis) + P(all 3 are cricket) + P(all 3 are squash)
= P(1st is tennis AND 2nd is tennis AND 3rd is tennis) + (1st is cricket AND 2nd is cricket AND 3rd is cricket) + P(1st is squash AND 2nd is squash AND 3rd is squash)
= [2/9 x 2/9 x 2/9] + [3/9 x 3/9 x 3/9] + [4/9 x 4/9 x 4/9]
= 8/9³ + 27/9³ + 64/9³
= 99/9³
= 11/9²
= 11/81

Answer: D

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Brent
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by Scott@TargetTestPrep » Mon May 06, 2019 7:14 pm
vaibhav101 wrote:a box contains 2 tennis, 3 cricket and 4 squash balls. 3 balls are drawn in succession with replacement. Find the probability that all 3 are of same type.

A 12/81
B 1/9
C 18/81
D 11/81
E none of these

The probability they are all tennis balls is 2/9 x 2/9 x 2/9 = 8/729.

The probability they are all cricket balls is 3/9 x 3/9 x 3/9 = 27/729.

The probability they are all squash balls is 4/9 x 4/9 x 4/9 = 64/729.

Therefore, the probability the 3 balls are of the same type is 8/729 + 27/729 + 64/729 = 99/729 = 11/81.

Answer: D

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