Final answer:
To calculate the probability of getting two cards with the same number out of 7 cards, we count the number of favorable outcomes and divide it by the total number of possible outcomes.
Step-by-step explanation:
To calculate the probability that the numbers on the two cards are the same, we need to count the number of favorable outcomes and divide it by the total number of possible outcomes.
There are 7 cards with numbers on them. If Harry picks the same number twice, it means he must choose one of the available cards with the same number. There are 3 cards with the number 2 and 5 cards with the number 3. Therefore, the number of favorable outcomes is 3 + 5 = 8.
The total number of possible outcomes is the number of ways Harry can choose 2 cards out of the 7 available. This can be calculated using the combination formula, which is nCr = n! / (r! * (n-r)!). In this case, n = 7 (number of cards) and r = 2 (number of cards Harry picks). Plugging in the values, we get 7! / (2! * (7-2)!) = 21.
So, the probability of the numbers on the two cards being the same is 8/21.