Question

if a fair coin is tossed four times, the probability of getting exactly three heads is

Explanation:

Step1: Calculate total number of outcomes

When a coin is tossed \(n = 4\) times, each toss has \(2\) possible outcomes (head or tail). So the total number of outcomes is \(N=2\times2\times2\times2 = 2^{4}=16\).

Step2: Calculate number of favorable outcomes

We use the binomial coefficient formula \(C(n,k)=\frac{n!}{k!(n - k)!}\), where \(n = 4\) (number of trials) and \(k = 3\) (number of heads).

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Step3: Calculate probability

The probability \(P\) of getting exactly \(k = 3\) heads is \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Substituting the values, we get \(P=\frac{4}{16}=\frac{1}{4}\).

Answer:

\(\frac{1}{4}\)