Question

You play two slot machines at the same time machine X is programmed to produce a winner 12% of the time and machine Y is programmed to produce a winner 7% of the time. Find the probability of winning at both machines if you play each machine onceFind the probability of losing at both machines if you play each machine once Answer the following problems using multiplication rule make sure to reduce your fraction

Answer 1

The probability of winning at both machines is 0.84% and the probability of losing at both machines is 99.16%.

Step-by-step explanation:

To find the probability of winning at both machines, we can use the multiplication rule. The probability of winning at machine X is 12% or 0.12, and the probability of winning at machine Y is 7% or 0.07. Since the plays of each machine are independent, we can multiply these probabilities together to find the probability of winning at both machines. Thus, the probability of winning at both machines is 0.12 * 0.07 = 0.0084, or 0.84%.

To find the probability of losing at both machines, we can subtract the probability of winning at both machines from 1, since the sum of all probabilities should equal 1. Therefore, the probability of losing at both machines is 1 - 0.0084 = 0.9916, or 99.16%.

Answer 2

The probability of two events happening one after another is the product of both probabilities.

The probability of winning at the machine X is 12/100 and the probability of winning at the machine Y is 7/100. Then, the probability of winning at both playing once at each machine, is:

`(12)/(100)*(7)/(100)=(84)/(10000)=(0.84)/(100)`

On the other hand, since the probability of winning at machine X is 12/100, then the probability of loosing is 88/100. Similarly, the probability of loosing at machine Y is 93/100. Then, the probability of loosing at both machines is:

`(88)/(100)*(93)/(100)=(8184)/(10000)=(81.84)/(100)`

Therefore, the probability of winning at both machines is 0.84% and the probability of loosing at both machines is 81.84%.