# Probability

Question

What is the expected no. of heads that come up when fair coin is flipped five times?

Answer 1

Probability of getting head exactly once = $5c_1 (1/2)^1 \times (1/2)^4 = 5/32$

Probability of getting head exactly twice = $5c_2 (1/2)^2 \times (1/2)^3 = 10/32$

Probability of getting head exactly thrice = $5c_3 (1/2)^3 \times (1/2)^2 = 10/32$

Probability of getting head exactly four times = $5c_4 (1/2)^4 \times (1/2)^1 = 5/32$

Probability of getting head exactly five times = $5c_5 (1/2)^5 \times (1/2)^0 = 1/32$

Expected no. of heads = 1*5/32 + 2 * 10/32 + 3*10/32 + 4*5/32 + 5*1/32 = $\frac{80}{32}= 2.5$

Comments

simply apply formula np = 5 * (1/2) = 2.5 answer here