1. ## Probability Question

Hi!
I really cannot work out how to solve this question, and a little bit of help would be much appreciated.

Q. Jake and Jessica are working on a problem. Jake has a 45% chance of solving it, and Jessica has a 65% chance of solving it. Find the probability that both solve the problem.

Thanks!

2. Originally Posted by Help me!!!
Hi!
I really cannot work out how to solve this question, and a little bit of help would be much appreciated.

Q. Jake and Jessica are working on a problem. Jake has a 45% chance of solving it, and Jessica has a 65% chance of solving it. Find the probability that both solve the problem.

Thanks!
These two events are independent. This is easiest solved using a tree diagram.

In this case, you need to remember two formulae:

$\displaystyle Pr(A') = 1 - Pr(A)$ and $\displaystyle Pr(A \cap B) = Pr(A) \times Pr(B)$.

If $\displaystyle Pr(Jake) = 0.45$ then $\displaystyle Pr(Jake') = 0.55$

And if $\displaystyle Pr(Jessica) = 0.65$ then $\displaystyle Pr(Jessica') = 0.35$.

So look at this tree diagram (attached), follow the branches that have both Jake and Jessica win, and multiply the corresponding probabilities.