Question

Four coins are tossed. Let M be the variable representing the number of heads that occur. Find the values of the rand om variable M and its corresponding probabilities

Answer 1

If 4 coins are tossed, then there can be from 0 to 4 heads. M has a binomial distribution with n = 4, p = 0.5, so

$P(M=0)={4 \choose 0}*({\frac 1 2})^4={\frac 1 {16}}$

$P(M=1)={4 \choose 1}*({\frac 1 2})^4={\frac 4 {16}}={\frac 1 4}$

$P(M=2)={4 \choose 2}*({\frac 1 2})^4={\frac 6 {16}}={\frac 3 8}$

$P(M=3)={4 \choose 3}*({\frac 1 2})^4={\frac 4 {16}}={\frac 1 4}$

$P(M=4)={4 \choose 4}*({\frac 1 2})^4={\frac 1 {16}}$