Question

probability of getting exactly two heads when flipping a penny, a nickel, and a dime at the same time

Answer 1

To find the probability of getting exactly two heads when flipping a penny, a nickel, and a dime, let's first identify the possible outcomes.

Each coin has two possible outcomes: Heads (H) or Tails (T). When you flip three coins, the total number of possible outcomes is \(2^3 = 8\). The outcomes can be listed as follows:

1. HHH
2. HHT
3. HTH
4. HTT
5. THH
6. THT
7. TTH
8. TTT

Next, we count the outcomes that have exactly two heads. The outcomes that have exactly two heads are:

1. HHT
2. HTH
3. THH

There are 3 outcomes that result in exactly two heads.

Now, to find the probability, we use the formula:

\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]

In this case, the number of favorable outcomes is 3, and the total number of outcomes is 8:

\[
\text{Probability} = \frac{3}{8}
\]

Thus, the probability of getting exactly two heads when flipping a penny, a nickel, and a dime is \(\frac{3}{8}\).