Question

suppose a bowl contains candies of various colors: 14 red, 8 blue, and 10 yellow. if two candies are chosen at random, find the probability that they are both red if they are chosen:

Answer 1

Explanation:

The probability of selecting two red candies from the bowl can be calculated by dividing the number of favorable outcomes (selecting two red candies) by the total number of possible outcomes (choosing any two candies from the bowl).

To find the probability, we need to determine the number of ways we can select two red candies from the 14 red candies in the bowl.

We can use the concept of combinations to calculate this. The number of ways to choose two items from a set of n items is given by the formula nC2, which is equal to n! / (2! * (n-2)!). In this case, n is equal to 14.

So, the number of ways to choose two red candies from the bowl is 14C2 = 14! / (2! * (14-2)!) = 14! / (2! * 12!).

Simplifying this expression, we get 14! / (2! * 12!) = (14 * 13) / (2 * 1) = 91.

Now, we need to calculate the total number of ways to choose any two candies from the bowl. Since there are 32 candies in total (14 red + 8 blue + 10 yellow), the number of ways to choose two candies from this set is 32C2 = 32! / (2! * (32-2)!) = 32! / (2! * 30!) = (32 * 31) / (2 * 1) = 496.

Finally, we can calculate the probability by dividing the number of favorable outcomes (91) by the total number of possible outcomes (496):

P(both candies are red) = 91 / 496 = 0.183467.

So, the probability of selecting two red candies from the bowl is approximately 0.183467, or 18.35%.