Alex has 0.7 chance of winning race A, 0.6 of winning B.

[greese]

Alex has a 0.7 chance of winning race A and a 0.6 chance of winning race B. What is the probability that he wins one race?

If I do a tree diagram my solution is as follows:

P = LW or WL
= 0.3*0.6 + 0.7*0.4
= 0.46

But if I use the P(A or B) = P(A) + P(B) - P(A & B)
= 0.7 + 0.6 - (0.7*0.6)
= 0.88

Which is correct and why?

Thanks

 

[Deleted member 4993]

Alex has a 0.7 chance of winning race A and a 0.6 chance of winning race B. What is the probability that he wins one race?

If I do a tree diagram my solution is as follows:

P = LW or WL <<< what about WW
= 0.3*0.6 + 0.7*0.4
= 0.46

But if I use the P(A or B) = P(A) + P(B) - P(A & B)
= 0.7 + 0.6 - (0.7*0.6)
= 0.88

Which is correct and why?

Thanks

 

[pka]

“Which is correct and why?”
Your second answer assumes that the two events are independent. Are they?
Moreover, that answer is for this: “wins at least one”.

Do you mean “exactly one”?
If so that is what you found in the first try, assuming independence.

 

[greese]

Let's assume the races are independent, thus P(one win only) = 0.46

Can you give me an example where the races would not be independent?

Pica, are you saying that if the events are independent, then the answer will be 0.88 provided the question asks for "the probability that Alex wins at least once."?

I am thinking yes because it would also right to answer this question based on P(at least once) = 1 - P(0 wins) = 1 - 0.3 * 0.4


Thanks again.

 

[pka]

Pica, are you saying that if the events are independent, then the answer will be 0.88 provided the question asks for "the probability that Alex wins at least once."?

YES.