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Question

Mathematics Question on Event

A coin is tossed 77 times. Each time a man calls head. Find the probability that he wins the toss on more occasions.

A

23\frac{2}{3}

B

12\frac{1}{2}

C

34\frac{3}{4}

D

13\frac{1}{3}

Answer

12\frac{1}{2}

Explanation

Solution

The man has to win at least 44 times.
∴\therefore Reqd. probability =
7C4(12)4.(12)3+7C5(12)5.(12)2+7C6(12)6.12+7C7(12)7^{7}C_{4} \left(\frac{1}{2}\right)^{4} .\left(\frac{1}{2}\right)^{3} + ^{7}C_{5} \left(\frac{1}{2}\right)^{5} . \left(\frac{1}{2}\right)^{2} + ^{7}C_{6} \left(\frac{1}{2}\right)^{6} . \frac{1}{2} + ^{7}C_{7} \left(\frac{1}{2}\right)^{7}
=(7C4+7C5+7C6+7C7).127=6427=12= \left(^{7}C_{4} + ^{7}C_{5} + ^{7}C_{6} + ^{7}C_{7}\right) . \frac{1}{2^{7}} = \frac{64}{2^{7}} = \frac{1}{2}