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

10
10

12
12
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1 answer

To determine how many times you would expect to select the card labeled "5" after repeating the experiment of selecting a card from a deck of 10 cards labeled 1-10 a total of 120 times, we can use the concept of expected value.

In a single selection, the probability of selecting the card labeled "5" is \( \frac{1}{10} \) since there is one favorable outcome (selecting card 5) out of 10 possible outcomes (cards 1 through 10).

If you repeat the experiment 120 times, the expected number of times you select card 5 is given by:

\[ \text{Expected number of times} = \text{total trials} \times \text{probability of selecting card 5} \]

\[ \text{Expected number of times} = 120 \times \frac{1}{10} = 12 \]

Therefore, you would expect to select the number 5 a total of 12 times.

So, the correct response is 12.