Question

An experiment is conducted with a bag of marbles containing 5 white and 2 blue marbles. The results of a marble being drawn twice and replaced 100 times are shown in the table.

Outcome Frequency
White, White 27
White, Blue 22
Blue, Blue 18
Blue, White 33

Find P(1 blue).
33 over 100
50 over 100
55 over 100
73 over 100

Answer 1

To find \( P(1 \text{ blue}) \), we need to consider the cases where exactly one blue marble is drawn in two draws. This occurs in two scenarios:

1. White followed by Blue (White, Blue)
2. Blue followed by White (Blue, White)

From the table, we can see the frequencies for these outcomes:
- Frequency of (White, Blue) = 22
- Frequency of (Blue, White) = 33

Now, we add these frequencies together to get the total frequency of outcomes with 1 blue marble:

\[
\text{Total frequency of 1 blue} = 22 + 33 = 55
\]

Next, we find the probability of drawing exactly 1 blue marble in 2 draws by dividing the total frequency of 1 blue by the total number of trials (which is 100).

So, we calculate:

\[
P(1 \text{ blue}) = \frac{55}{100}
\]

Therefore, the probability \( P(1 \text{ blue}) \) is:

\[
\frac{55}{100}
\]

Thus, the correct answer is **55 over 100**.