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 com falls heads, he answers true1; if it falls tails, he answers false1. Find the probability that he answers at least 12 questions correctly.

Explanation

Probability that student answers a question true = `1/2`

i.e., when a coin is thrown, probability that a head is obtained = `1/2`

Probability that his answer is false = `1 (-1)/2 =1/2`

Probability that his answer at least 12 questions correctly = `P (12) + P (13) + P (14) +…….. P (20)`


`=^20 C^12( 1/2)^20+ 20^C^13( 1/2)^20+...+^20 C^20( 1/2)^20`


`=(1/2)^20⋅[^20C^12+ 20^C^13 +...+^20C^20]`