Question

lindsay is going to the gym to use either a stairmaster or a stationary bike. she would prefer the stairmaster, but using a bike is acceptable as well. the probability of getting a stairmaster is .20. given that she gets the stairmaster, the probability that she will have it for forty minutes straight is .10. given that she gets a bike, the probability is 0.50 that she will be able to use it for forty minutes straight. what is the probability that lindsay worked out for forty minutes straight today?

Answer 1

The probability that Lindsay worked out for forty minutes straight today is 0.42.

Step-by-step explanation:

To find the probability that Lindsay worked out for forty minutes straight, we need to consider two cases: when she gets a stairmaster and when she gets a stationary bike.

Firstly, the probability of getting a stairmaster is 0.20, and given that she gets a stairmaster, the probability of having it for forty minutes straight is 0.10.

So the probability of getting a stairmaster and using it for forty minutes straight is 0.20 * 0.10 = 0.02.

Secondly, the probability of getting a bike is 0.80 (1 - 0.20), and given that she gets a bike, the probability of using it for forty minutes straight is 0.50.

So the probability of getting a bike and using it for forty minutes straight is 0.80 * 0.50 = 0.40.

Therefore, the overall probability that Lindsay worked out for forty minutes straight today is 0.02 + 0.40 = 0.42.