a coin is tossed twice in a row. what is the probability of tossing \heads\ both times?\na $\frac{1}{4}$\nb…

Explanation:

Step1: Determine probability of single - toss

The probability of getting heads in a single fair coin - toss is $\frac{1}{2}$ since there are 2 possible outcomes (heads or tails) and 1 favorable outcome (heads).

Step2: Use multiplication rule for independent events

Since the two coin - tosses are independent events, the probability of two independent events $A$ and $B$ both occurring is $P(A\cap B)=P(A)\times P(B)$. Here, $A$ is the event of getting heads on the first toss and $B$ is the event of getting heads on the second toss. So $P(A) = P(B)=\frac{1}{2}$, and $P(A\cap B)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

A. $\frac{1}{4}$