Probability homework

Question

Help!

A recent survey by the cancer society has shown that the probability that someone is a smoker is P(S)= 0.39. They Have also determined that the probability that someone has lung cancer, given that they are a smoker is P(LC|S)= 0.205. What is the probability that a random person is a smoker and has lung cancer?

A. 0.53

B. 0.08

C. 0.03

D. 0.07

Answer 1

Hi Leah,

you need to know this formula: p(A/B) = p(A and B) / p(B)

now you choose A/B = Lc/s. and B = s

replace given information to the formula

0.205 = p(Lc and s) / 0.39. Both side times 0.39

0.205 . 0.39 = p( Lc and s)

0.07995 = answer

after rounding 0.08

i hope it is useful, please tell me know if you have any question.

Minoo

Answer 2

Givens:

P(S)=0.39; this means that 39% of the population smokes

P(LC|S)=0.205; this means that 20.5% of SMOKERS have lung cancer

So, 20.5% of 39% of the population both smoke and have lung cancer. That is 0.205*0.39=0.07995= 7.995% of the general population both smoke and have lung cancer.

ANS:7.995%