Answer:
a. 0.63
b. 0.33
Explanation:
Here is a probability question. When two events are independent, it means that the probability of one of the events happening has no effect on the probability on the other happening.
From the question, let P(H) be the probability of passing the history course while P(E) is the probability of passing the English course;
By representation;
P(H) = 0.75
P(E) = 0.84
a) Probability of passing both
This means that he passes history and also passes English;
Mathematically that would be represented as;
P(E) * P(H) = 0.84 * 0.75 = 0.63
b) Probability that he passes exactly one of the courses.
This means that he passes one and he fails the other. Mathematically, we should remember that the probability of an event not happening = 1 - probability of the event happening
Let P’(H) and P’(E) be the probability of failing the history and english courses respectively;
Thus; P’(H) = 1 - 0.75 = 0.25
while P’(E) = 1-0.84 = 0.16
Now the probability that he passes exactly one means he passes one and fails the other.
So in this case, we have two scenarios; He passes History and fail English or passes English and fails history.
Thus, we have;
[P(H) and P’(E) or P(E) and P’(H)]
In probability, and means multiplication while or means addition; thus we have;
{P(H) * P’(E) } + {P’(H) * P(E)}
= ( 0.75 * 0.16) + (0.25 * 0.84)
= 0.12 + 0.21 = 0.33