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

110
Start Fraction 1 over 10 End Fraction

1120
Start Fraction 1 over 120 End Fraction

12
12

10

1 answer

To find the expected number of times you would select the card labeled "5" when drawing from a shuffled deck of 10 cards (labeled 1 to 10) over 120 trials, you can use the concept of expected value.

The probability of selecting the card labeled "5" in one trial is:

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

Now, to find the expected number of times you will select the card "5" in 120 trials, you multiply the probability by the number of trials:

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

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

12

So the correct response is 12.