Question

A deck of 10 cards labeled 1–10 is shuffled. One card is selected at random. If the experiment is repeated 120 times, how many times will you expect to select number 5?(1 point)
Responses

12
12

110
Start Fraction 1 over 10 End Fraction

10
10

1120
Start Fraction 1 over 120 End Fraction

Answer 1

To find the expected number of times you will select the number 5 when you select a card 120 times from a deck of 10 cards (labeled 1 to 10), you can use the probability of selecting the number 5.

The probability of selecting the number 5 from the deck is:

\[
P(\text{selecting 5}) = \frac{1}{10}
\]

If you are repeating this selection 120 times, the expected number of times you will select the number 5 can be calculated by multiplying the probability of selecting 5 by the number of trials (which is 120):

\[
\text{Expected number of times selecting 5} = P(\text{selecting 5}) \times \text{Number of trials} = \frac{1}{10} \times 120 = 12
\]

Therefore, the expected number of times you will select the number 5 is:

**12**.