Questions: Suppose you flip two coins. What is the probability of getting at most one heads? Give your answer as a reduced fraction.

Solution Steps

We need to find the probability of getting at most one head when flipping two coins. This can be expressed mathematically as \( P(X \leq 1) \), where \( X \) is the number of heads obtained.

Using the binomial probability formula:

\[ P(X = x) = \binom{n}{x} \cdot p^x \cdot q^{n-x} \]

For \( n = 2 \) (number of trials), \( x = 0 \) (number of successes), \( p = 0.5 \) (probability of heads), and \( q = 0.5 \) (probability of tails), we have:

\[ P(X = 0) = \binom{2}{0} \cdot (0.5)^0 \cdot (0.5)^{2} = 1 \cdot 1 \cdot 0.25 = 0.25 \]

Thus, the probability of getting exactly 0 heads is \( 0.25 \).

Using the same formula for \( x = 1 \):

\[ P(X = 1) = \binom{2}{1} \cdot (0.5)^1 \cdot (0.5)^{1} = 2 \cdot 0.5 \cdot 0.5 = 0.5 \]

Thus, the probability of getting exactly 1 head is \( 0.5 \).

To find the probability of getting at most 1 head, we sum the probabilities of getting exactly 0 heads and exactly 1 head:

\[ P(X \leq 1) = P(X = 0) + P(X = 1) = 0.25 + 0.5 = 0.75 \]

Final Answer