Coin Toss Probability

Question

What is the probability that in 7 coin tosses we get exactly 5 heads and 2 tails? Do NOT round.

Answer 1

Here, the formula P(X = x) equal to [n! ÷ x! ÷ (n − x)!] × p^x × (1 − p)^{(n − x)}

translates to P(X = 5) = [7! ÷ 5! ÷ (7 − 5)!] × 0.5⁵ × (1 − 0.5)^{(7 − 5)} (for a fair

coin with equal or one-half probability of landing on either side).

Then write [7 × 6 ÷ 2] × 0.5⁵ × (1 − 0.5)^{(7 − 5)} which goes to 21 × (1/2)⁷ or 21/128

(equal to 0.1640625).