3 students will represent your school at a conference at the state capital. A drawing will be held to select the 3 representatives from a group of 5 finalsts. If you and your friend are both finalists, what are the chances that both of your names will be drawn?
Is it 2 out of 5 chance? Not sure how to figure this one.
Thank you
Think of the possible combinations of 3 that can be drawn from 5. Number the students from 1 to 5. Here are the possibilities. Since the order of selection is not important, you are dealing with combinations rather than permutations. In other words, order is not important.
123, 124, 125, 234, 235, 345, 145, 245, 134 and 135.
Assuming that you and your friends are 1 and 2, what are the chances of you both being drawn?
I hope this helps. Thanks for asking.
To find the chances of both you and your friend being drawn as representatives, you need to determine the number of favorable outcomes (combinations where both of your names are drawn) and the number of possible outcomes (all possible combinations of 3 students drawn from the 5 finalists).
From the list of possible combinations, we can see that there are 10 different combinations. In 2 of these combinations (12 and 21), both you and your friend are selected.
Therefore, the chances of both of your names being drawn is 2 out of the 10 possible combinations.
To simplify, this can be expressed as a probability: 2/10 = 1/5 = 0.2.
So, the chances are 1 in 5, or 20 percent, that both you and your friend will be selected as representatives.