NCERT Class XII Mathematics Chapter - - Solutions
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Question : 89
Total: 101
A die is thrown again and again until three sixes are obtained. Find theprobability of obtaining the third six in the sixth throw of the die.
Solution:
Let p be probability of getting a six =
q be probability of not getting a six= 1 −
=
∴ X has a binomial distribution withn = 5 , p =
, q =
∴ P ( X = r ) = n C r ( q ) n − r p r
⇒ P (obtaining the third six in sixth throw)
= P(2 success in the first 5 throws) × P(success in 6th throw)= ( 5 C 2 q 3 p 2 ) p
= 5 C 2 (
) 3 (
) 2 ×
=
q be probability of not getting a six
∴ X has a binomial distribution with
⇒ P (obtaining the third six in sixth throw)
= P(2 success in the first 5 throws) × P(success in 6th throw)
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