Question

@terenzreignz Could you help me with this one too? =)
A meteorologist reported an 82% chance the weather would be sunny and a 74% chance it would be sunny and that the temperature would get over 85 °F. If it is a sunny day, what is the probability the temperature will also be more than 85 °F?
a. 31.7%
b. 74.0%
c. 90.2%
d. 18.0%

Answer 1

This is a little tricky. We need what's called 'conditional' probabilities...
\[\Large Pr(A|B) = \frac{Pr(A \ and \ B)}{Pr(B)}\]

Answer 2

To translate...
Probability of event A happening given that event B happens is equal to the probability of both A and B happening divided by the probability of B happening.

Answer 3

So here, our event A is that the temperature would go over 85 degrees.
Our event B is that it would be sunny.

So, (A|B) is the probability of the temperature going over 85 degrees given that it is sunny.

Okay?

Answer 4

Got it!

Answer 5

So, what's the probability that both A and B occur? (IE, that it is both sunny and the temperature goes over 85?)

Answer 6

she said she got it yo

Answer 7

I suppose.

Answer 8

I think the answer is C. =)

Answer 9

Well, who said it wasn't? :P
\[\Large Pr(A \ and \ B) = 0.74\]\[\Large Pr(B) = 0.82\]

\[\Large Pr(A|B) = \frac{Pr(A \ and \ B)}{Pr(B)}=\frac{0.74}{0.82}\approx0.9024 \approx90.2\%\]

Answer 10

Thank you very much for your help!

Answer 11

thank you for answering her problem, @terenzreignz