Question

A deck of cards contains red, blue, orange, and yellow cards. A card is drawn and then replaced. This process is carried out 40 times. The results are shown in the table.
Results
Color
Frequency
Red: 9
Blue: 8
Orange: 13
Yellow:10

Based on these results, what is the experimental probability that the next card drawn is red or orange?

Answer 1

To find the experimental probability that the next card drawn is red or orange, we first need to determine the total number of draws and the number of favorable outcomes (drawing either a red or orange card).

Based on the results provided:

- Red cards drawn: 9
- Orange cards drawn: 13
- Total draws: 40

Now, we can calculate the number of favorable outcomes by adding the frequencies of red and orange cards:

\[
\text{Favorable outcomes} = \text{Red} + \text{Orange} = 9 + 13 = 22
\]

Next, we calculate the experimental probability of drawing either a red or orange card. The formula for experimental probability is:

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

Substituting in the values we found:

\[
\text{Probability} = \frac{22}{40}
\]

To simplify this fraction:

\[
\frac{22}{40} = \frac{11}{20}
\]

Thus, the experimental probability that the next card drawn is red or orange is:

\[
\frac{11}{20}
\]