Question

A refrigerator contains 4 cans of diet soda and 6 cans of regular soda. if two cans of soda are randomly selected without​ replacement, determine the probability that both cans selected are diet soda. use combinations to determine the probability. question content area bottom part 1 the probability that both cans selected are diet soda is enter your response here. ​(type an integer or a simplified​ fraction.)

Answer 1

The probability that both cans selected are diet soda is 2/15 when using combinations to calculate the likelihood.

Step-by-step explanation:

To determine the probability that both cans selected are diet soda, we can use the concept of combinations. The formula for combinations is C(n, k) = n! / (k!(n-k)!), where 'n' represents the total number of items to choose from, 'k' is the number of items we want to choose, and '!' denotes factorial.

First, calculate the number of ways to choose 2 diet sodas out of 4, which is C(4, 2). This is 4! / (2!(4-2)!) = 6.

Next, calculate the total number of ways to choose 2 cans out of the total 10 cans, which is C(10, 2). This is 10! / (2!(10-2)!) = 45.

Finally, the probability is the number of ways to choose 2 diet sodas divided by the total number of ways to choose 2 cans, which is 6/45, simplifying to 2/15.