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 `=frac{1}{2}`

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

Probability that his answer is false` =1-frac{1}{2}=frac{1}{2}`

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

`=^{20} C_{12}(frac{1}{2})^{8}(frac{1}{2})^{12}+^{20} C_{13}(frac{1}{2})^{7} `

`(frac{1}{2})^{13}+cdots ldots cdot^{20} C_{20}(frac{1}{2})^{20}`

`=(frac{1}{2})^{20}[^{20} C_{12}+^{2} C_{13}+^{20} C_{14}+cdots ldots cdot^{20} C_{20}]`