Math Help - Multiplication Rule

1. Multiplication Rule

Mark experiences difficulty in starting his two cars. The probability that the first starts is .80 and the probability that the second starts is .40. There is a probability of .30 that both cars start. What is the probability that at least one of the two starts?

2. Originally Posted by tdvc006
Mark experiences difficulty in starting his two cars. The probability that the first starts is .80 and the probability that the second starts is .40. There is a probability of .30 that both cars start. What is the probability that at least one of the two starts?
I am rather confused if the probability the .8 and the other is .4 then should the other one not be .32? Anyways maybe this has something to do with them not being disjoint.

This is what you want:
1)First Starts Second Does Not
2)First Does Not Second Does
3)First Starts Second Starts

The probability of Not Car one is .2
The probability of Not Care two is .6

Thus, the probability of 1) is (.8)(.6)=.48
Thus, the probability of 2) is (.2)(.4)=.08
Thus, the probability of 3) is (.30) =.30

Add them up to get, 86%

3. If the probability of A and B hapening is not the product of the probability of A and the probability of B, then this tells you that A and B are not independent.

There are 4 events here. Let A' denote not-A etc. They are AB, A'B, AB' and A'B'. You are told that p(A) = 0.8 = p(AB) + p(AB'), that p(B) = 0.4 = p(AB) + p(A'B) and that p(AB) = 0.3. Hence p(AB') = 0.5, p(A'B) = 0.1 and p(AB) + p(A'B) + p(AB') = 0.9.