Question

The list below shows all of the possible outcomes for flipping four coins.

HHHH
HHHT
HHTH
HHTT
HTHH
HTHT
HTTH
HTTT
THHH
THHT
THTH
THTT
TTHH
TTHT
TTTH
TTTT

What is the probability of getting the same number of heads and tails?
StartFraction 1 over 8 EndFraction
One-fourth
StartFraction 3 over 8 EndFraction
Three-fourths

Answer 1

To determine the probability of getting the same number of heads and tails when flipping four coins, we first need to identify the outcomes where the number of heads equals the number of tails.

When flipping four coins, there are a total of \(2^4 = 16\) possible outcomes. We want to find the outcomes where there are 2 heads and 2 tails.

The combinations of 2 heads out of 4 flips can be calculated using the binomial coefficient \(\binom{n}{k}\), where \(n\) is the total number of coins (flips), and \(k\) is the number of heads (or tails) we want. In this case, we are calculating \(\binom{4}{2}\):

\[
\binom{4}{2} = \frac{4!}{2!(4-2)!} = \frac{4 \times 3}{2 \times 1} = 6
\]

Now, let's list out the successful outcomes where there are 2 heads and 2 tails:

1. HHTT
2. HTHT
3. HTTH
4. THHT
5. THTH
6. TTHH

There are 6 outcomes with 2 heads and 2 tails.

Next, we calculate the probability:

\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{6}{16} = \frac{3}{8}
\]

Thus, the probability of getting the same number of heads and tails from flipping four coins is \(\frac{3}{8}\).

The correct answer choice is:
\[
\frac{3}{8}
\]