Question

Paul has 8 cards. There is a number on each card. 2 3 3 5 5 5 5 Paul takes at random 3 of the cards. He adds together the 3 numbers on the cards to get a total T. Work out the probability that T is an odd number. (4 marks )

Answer 1

To find the probability that the total T is an odd number, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes. The probability is 1/28.

Step-by-step explanation:

In this scenario, Paul has 8 cards with numbers 2, 3, 3, 5, 5, 5, and 5. He randomly selects 3 cards and adds their numbers together to get a total T. We need to determine the probability that T is an odd number.

To solve this, we first need to find the total number of possible outcomes when selecting 3 cards from the 8 cards. The formula to calculate this is 8 choose 3 which is denoted as C(8, 3) or 8C3. It can be calculated as:

C(8, 3) = 8! / (3! * (8-3)!) = 8! / (3! * 5!) = (8 * 7 * 6) / (3 * 2 * 1) = 56

Now, we need to find the number of favorable outcomes where T is an odd number. There are two possibilities:

1. Selecting three odd numbers (3, 3, 5)

2. Selecting one even number (2) and two odd numbers (3, 5)

Hence, the number of favorable outcomes is 1 (for three odd numbers) + 1 (for one even and two odd numbers), which equals 2.

Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = Number of favorable outcomes / Total number of possible outcomes = 2 / 56 = 1/28