Frank has a 65% chance of receiving an A grade in geology, a 60% chance of receiving an A grade in mathematics, and a 77% chance of receiving an A grade in geology or mathematics (or both). Find the probability that he receives A grades in both geology and mathematics.
I get: P(geo and math) = P(geo) + P(math) - P(geo or math)
= 0.65 + 0.60 - 0.77
= 1.25 - 0.77
= 0.48
You need to make up your mind. Is the .77 for both or either-or?
I would assume that the above data (.77) is not needed.
To find the probability of both/all events occurring you need to multiply the probability of the individual events.
.65 * .60 = .39
To find the probability that Frank receives A grades in both geology and mathematics, you can use the formula for the probability of the intersection of two events.
Let's call the event of Frank receiving an A grade in geology "G" and the event of Frank receiving an A grade in mathematics "M". We want to find the probability of both G and M occurring, denoted as P(G and M).
According to the problem, the probability of Frank receiving an A grade in geology is 65% or 0.65. Similarly, the probability of Frank receiving an A grade in mathematics is 60% or 0.60.
However, we also know that the probability of Frank receiving an A grade in geology or mathematics (or both) is 77% or 0.77.
We can use these probabilities to find the probability of both G and M occurring:
P(G and M) = P(G) + P(M) - P(G or M)
Substituting the given values:
P(G and M) = 0.65 + 0.60 - 0.77
= 1.25 - 0.77
= 0.48
Therefore, the probability that Frank receives A grades in both geology and mathematics is 0.48 or 48%.