Question

Find each probability if a coin is tossed 4 times. (Lesson 12-8)

P(exactly 2 heads).

Short answer

P(exactly 2 heads) = 0.375.

Step-by-step solution

Step 1. Given

A coin is tossed 4 times.

Step 2. To determine

P(exactly 2 heads).

Step 3. Calculation

Total number of tosses = n = 4

Probability of getting a head in each toss = p = 0.5

The number of heads = X = 2.

X follows a binomial distribution with n = 4 and p = 0.5.

So,

$\begin{array}{l}P\left(\text{exactly2heads}\right)\\ =P\left(X=2\right)\\ =\left(\begin{array}{c}4\\ 2\end{array}\right){\left(0.5\right)}^2{\left(1-0.5\right)}^{4-2}\\ =0.375\end{array}$

Hence, P(exactly 2 heads) = 0.375.