There are 4 cardio stations and 6 weight lifting stations at the gym. You decide to choose 4 stations randomly for today's workout. What is the probability you choose all weight lifting or all cardio stations?

Answer 1

First, let's calculate the total number of ways to choose 4 stations out of the 10 total stations.

Total number of ways = 10 choose 4 = 10! / (4!(10-4)!) = 210.

Next, let's calculate the number of ways to choose all weight lifting stations.

Number of ways to choose all weight lifting stations = 6 choose 4 = 6! / (4!(6-4)!) = 15.

Finally, let's calculate the probability of choosing all weight lifting stations.

Probability = Number of ways to choose all weight lifting stations / Total number of ways = 15/210 = 0.0714.

Therefore, the probability of choosing all weight lifting stations for today's workout is 0.0714 or 7.14%.

Similarly, the probability of choosing all cardio stations is also 0.0714 or 7.14%.