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.