GATE Overflow Test Series | Probability | Test 1 | Question: 9

Question

A fair coin is tossed $8$ times. What is the probability that we get exactly $6$ heads?

• A. $\frac{7}{64}$
• B. 0.0109
• C. $\frac{\binom{8}{6}\times \binom{8}{2}}{2^{8}}$
• D. None of the above

Answer 1

The coin toss value follows discrete binomial distribution and we need to find $P(X = 6)$

$P(X = 6) = \frac{\binom{8}{6}}{2^{8}} =\frac{\binom{8}{2}}{256} = \frac{7}{64}$

Answer 2

A fair coin is tossed 8 times

a coin have 2 possibility=(H,T)

So total probability = 2^8

probability that we get exactly 6 heads = 8C6

So Required probability = 8C6  / 2^8

                                      = 8C2   / 2^8

                                      = (8! / 2! 6! ) / 2^8                 (nCr= n!/r!(n-r)!)

                                      = 7 / 64

I hope my answer helps you a lot.