Question

When a coin is tossed 4 times, what is the probability of getting at most 3 heads?

• A. 0.25
• B. 0.9375
• C. 0.6875
• D. 0.1

Hint:

When calculating probabilities for events like this, it's helpful to use the binomial distribution formula to calculate the number of favorable outcomes.

Answer 1

The Correct Option is B

When a coin is tossed 4 times, the total number of possible outcomes is $2^4 = 16$. The number of outcomes where we get 3 or fewer heads (i.e., 0, 1, 2, or 3 heads) can be found using the binomial distribution: The number of ways to get exactly $k$ heads in $n$ tosses is given by the binomial coefficient $\binom{n}{k}$. For 4 tosses: - 0 heads: $\binom{4}{0} = 1$ outcome - 1 head: $\binom{4}{1} = 4$ outcomes - 2 heads: $\binom{4}{2} = 6$ outcomes - 3 heads: $\binom{4}{3} = 4$ outcomes Thus, the total number of favorable outcomes is $1 + 4 + 6 + 4 = 15$. Therefore, the probability of getting at most 3 heads is: \[ P(\text{at most 3 heads}) = \frac{15}{16} = 0.9375 \] Thus, the correct answer is (2).