Question

A coin is tossed 8 times find probability that it shows heads atleast 5 times

Answer 1

=> As the coin is tossed 5 times, the total no. of probability is 2^8 = 256.

=> Now, let head be H and tail be T.

=> One possibility of tossing with 5 heads is givem below:

HHHHHTTT

Here the no. of chances of showing 5 heads is 8C5 =

$\frac{8!}{5! \times 3!} \\ \\ 8 \times 7 \\ \\ 56$

The question is of atleast 5 heads. So we have to find chances of getting 6 heads, 7 heads and 8 heads too.

=> No. of chances of getting 6 heads = 8C6 =

$\frac{8!}{6! \times 2!} \\ \\ 4 \times 7 \\ \\ 28$

=> Okay, the no. of chances of getting 7 and 8 heads are 8C7 = 8 and 8C8 = 1 respectively.

=> Sum of chances,

56 + 28 + 8 + 1 = 93

=> Probability = 93 / 256.