If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
Either-or probabilities are found by adding the individual probabilities.
I will do one problem for you, so you can see the process.
b) .7 * (1-.8) = .7 * .2 = .14
.8 * (1-.7) = .8 * .3 = .24
.14 + .24 = .38
Jen figures she has a 70% chance of passing math and an 80% chance of passing history
a) What is the probability that she passes math and history? What assumption did you have to make to answer this question?
b) What is the probability that she will pass one but not both? Note: There are two different ways that this can happen. Find the probability of both.
c) What is the possibility that she will pass neither?
d) Is there any other possible outcome for Jenn, other than those listed in a, b and c? What should the three probabilities in a, b and c add up to? Do your probabilities add up correctly?
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