Question

Find each probability if a coin is tossed 4 times.

P(at least 1 heads).

Short answer

P(at least 1 heads) = 0.9375.

Step-by-step solution

Step 1. Given

A coin is tossed 4 times.

Step 2. To determine

P(at least 1 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 ≥ 1.

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

So,

$\begin{array}{l}P\left(\text{atleast1heads}\right)\\ =P\left(X\ge 1\right)\\ =1-P\left(X=0\right)\\ =1-\left(\begin{array}{c}4\\ 0\end{array}\right){\left(0.5\right)}^0{\left(1-0.5\right)}^{4-0}\\ =1-0.0625\\ =0.9375\end{array}$

Hence, P(at least 1 heads) = 0.9375.