Question

a coin will be flipped three times. the result of each flip is either heads (h) or tails (t). the outcome hth represents the first result is heads, the second result is tails, and the third result is heads. the list of all possible outcomes is shown. each outcome is equally likely. hhh, hht, hth, htt, thh, tht, tth, ttt if the result of the first flip is tails, what is the probability that the coin lands on heads two times? a. $\frac{1}{4}$ b. $\frac{1}{3}$ c. $\frac{3}{8}$ d. $\frac{1}{2}$

Explanation:

Step1: Identify relevant outcomes

When the first - flip is tails, the possible outcomes are: THT, TTH, TTT, THH. So there are 4 possible outcomes when the first flip is tails.

Step2: Count favorable outcomes

The favorable outcomes (where there are two heads) among those with first - flip tails is THH. So there is 1 favorable outcome.

Step3: Calculate probability

The probability formula is $P=\frac{\text{Number of favorable outcomes}}{\text{Number of total outcomes}}$. Here, $P = \frac{1}{4}$.

Answer:

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