anonymous one year ago plzzzz i really dont kno how to do thisIn a factory, the chance that a certain machine works without overheating in the morning is 50%. If it runs smoothly all morning, then there is an 85% chance that it will continue for the rest of the day and a 15% chance that it will stop due to overheating. What is the probability that on a given day it will work in the morning and overheat later on?

1. misty1212

HI!!

2. misty1212

oh 'and" overheat i thought it said "or" lets see

3. misty1212

$P(A\cap B)=P(A)\times P(B|A)$

4. misty1212

if we put A = work in the morning then $$P(A)=0.5$$

5. misty1212

you are told that $P(B|A)=0.15$so we can multiply to find the answer