Statistics need answer before 1:35 CST

Question

The chance you have cancer is 1/100.
There is a cancer test.
The probability that the test will read yes if you DO have cancer is 90%.
The probability that the test will read positive if you do not have cancer is 7%.
What is the chance the test will read yes if you take it?
I got 7.83% but I'm not sure.

Answer 1

P(c) = .01 P(~c) = .99

P(+/c) = .90, P(-/c) = .10

P(+/~c) = .07 P(-/~c) = .93

P(+) = P(+/c)P(c) + P(+/~c)P(~c) = .9(.01) + .07(.99) = .009 + .000693 = .009693 = 0.9693% chance of testing positive if you take the test

what is P(+) = probability test result will be positive for cancer if you take it= 0.9693%

or

Use Bayes Theorem: P(a/b)P(b) = P(b/a)P(a) let a=+, b=c and solve for P(a)

P(a)= P(a/b)P(b)/P(b/a) = P(+/c)P(c)/P(c/+) = .9(.01)/P(c/+)= .009/P(c/+)= .009/.9285 = 0.009693 = .9693%

find P(c/+) = 1 -P(~c/+)= about .9285