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.
P(geo and math) = P(geo) + P(math) - P(geo or math)
= 0.65 + 0.60 - 0.77
= 1.25 - 0.77
= 0.48
To find the probability that Frank receives A grades in both geology and mathematics, we need to use the formula:
P(geo and math) = P(geo) + P(math) - P(geo or math)
First, we calculate P(geo), which is the probability of Frank receiving an A grade in geology, which is 65% or 0.65.
Next, we calculate P(math), which is the probability of Frank receiving an A grade in mathematics, which is 60% or 0.60.
Then, we calculate P(geo or math), which is the probability of Frank receiving an A grade in geology or mathematics (or both), which is given as 77% or 0.77.
Finally, we substitute these values into the formula:
P(geo and math) = 0.65 + 0.60 - 0.77
Now we can solve for the probability that Frank receives A grades in both geology and mathematics:
P(geo and math) = 1.25 - 0.77
By subtracting 0.77 from 1.25, we get 0.48.
Therefore, the probability that Frank receives A grades in both geology and mathematics is 0.48, or 48%.