A scout leader is going to pair a new member with one of the existing 15 troop members. Five of the boys love to go camping, ten like to fish, three enjoy archery, twelve like to go hiking, and one boy enjoys carving. What is the probability the new boy will be paired with a boy who does not love camping?
To find the probability that the new boy will be paired with a boy who does not love camping, we need to determine the number of troop members who do not love camping.
Out of the 15 existing troop members:
- Five boys love camping, so there are 15 - 5 = 10 boys who do not love camping.
Therefore, there are 10 possible choices for the scout leader to pair the new boy with out of the 15 existing troop members.
The probability can be calculated as:
Number of favorable outcomes / Total number of possible outcomes
In this case, the number of favorable outcomes is 10 (pairing with a boy who does not love camping), and the total number of possible outcomes is 15 (the total number of existing troop members).
So, the probability the new boy will be paired with a boy who does not love camping is 10/15, which simplifies to 2/3, or approximately 0.6667.
To find the probability of the new boy being paired with a boy who does not love camping, we need to determine the number of boys who do not love camping and divide it by the total number of boys.
From the given information, we know that there are 15 existing troop members. Out of these, five love camping, meaning there are 15 - 5 = 10 boys who do not love camping.
Therefore, the probability of the new boy being paired with a boy who does not love camping is 10 (boys who do not love camping) / 15 (total number of boys) = 2/3 or approximately 0.667.
So, the probability is 2/3 or approximately 0.667.