Question

Suppose there are 15 chairs in a room. Ten of the chairs have cushions, and five do not. Of the chairs with cushions, seven are old, and three are new. What is the probability of sitting in a chair that has an old cushion?









70%
52%
47%
55%

Answer 1

To find the probability of sitting in a chair that has an old cushion, we need to consider the number of chairs with old cushions and the total number of chairs.

**Step 1: Count the total number of chairs.**
- Total chairs = 15 (10 with cushions + 5 without cushions)

**Step 2: Count the number of chairs with old cushions.**
- Chairs with cushions: 10
- Old cushioned chairs: 7

**Step 3: Calculate the probability.**
The probability \(P\) of sitting in a chair that has an old cushion is given by the formula:

\[
P(\text{Old Cushioned Chair}) = \frac{\text{Number of Old Cushioned Chairs}}{\text{Total Number of Chairs}}
\]

Thus,

\[
P(\text{Old Cushioned Chair}) = \frac{7}{15}
\]

**Step 4: Convert the fraction to a percentage.**
To convert \(\frac{7}{15}\) into a percentage:

\[
\frac{7}{15} \approx 0.4667 \quad \text{(when calculated)}
\]

Then, multiply by 100 to get the percentage:

\[
0.4667 \times 100 \approx 46.67\%
\]

**Step 5: Match with the options.**
The closest percentage to \(46.67\%\) from the provided options is:

- 47%

Thus, the probability of sitting in a chair that has an old cushion is **47%**.