NCERT Class XII Mathematics Chapter - - Solutions
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Question : 74
Total: 101
In an examination, 20 questions of true-false type are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers ‘true’; if it falls tails, he answers ‘false’. Find the probability that he answers at least 12 questions correctly
Solution:
Let p be the probability of success that coin falls heads =
⇒ p =
, q =
X has binomial distribution withn = 20 , p =
, q =
∴ P ( X = r ) = n C r ( q ) n − r p r
∴ Required probability = P(he answers at least 12 questions correctly)
= P(X = 12) + P(X = 13) + ............. + P(X = 20)
= 20 C 12 (
) 8 (
) 12 + . . . . + 20 C 20 (
) 20
= (
) 20 [ 20 C 12 + 20 C 13 + . . . . + 20 C 20 ]
X has binomial distribution with
∴ Required probability = P(he answers at least 12 questions correctly)
= P(X = 12) + P(X = 13) + ............. + P(X = 20)
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