The probability that Jack plays guitar on a raining day is 0.6 and on a sunny day is 0.5. The probability that is rains tomorrow is 0.8. Find the probability that Jack will not play guitar tomorrow?

Is it 32%?

.8*.6 + .5(.2) = .48 + .1 = .58

1-.58 = .42

how did you get .1?

.5 (1-.8) = .5 * .2 = .1

probability that it will not rain tomorrow = 1 - probability that it will rain tomorrow
= 1 - .8

Thank you

To find the probability that Jack will not play guitar tomorrow, we need to consider two possibilities: it rains or it doesn't rain.

1. Let's find the probability that it rains tomorrow:
The probability of raining is given as 0.8. Therefore, the probability that it doesn't rain is (1 - 0.8) = 0.2

Given that Jack plays guitar with a probability of 0.6 on a raining day, the probability that he doesn't play guitar on a raining day is (1 - 0.6) = 0.4.

So, the overall probability that it rains tomorrow and Jack doesn't play guitar is 0.8 * 0.4 = 0.32.

2. Now, let's find the probability that it doesn't rain tomorrow:
The probability that it doesn't rain is 0.2.

Given that Jack plays guitar with a probability of 0.5 on a sunny day, the probability that he doesn't play guitar on a sunny day is (1 - 0.5) = 0.5.

So, the overall probability that it doesn't rain tomorrow and Jack doesn't play guitar is 0.2 * 0.5 = 0.1.

Now, we add the probabilities of both scenarios to get the total probability that Jack will not play guitar tomorrow:
0.32 + 0.1 = 0.42.

Therefore, the probability that Jack will not play guitar tomorrow is 0.42, or 42%.

So, the correct answer is not 32%, but 42%.