Hi everyone I have a question about probability: Fair die thrown two times, final score is calculated as follows. If the number on the second throw is a 5 he multiplies the two numbers together, and if the number on the second throw is not a 5 he adds the two numbers together.
What is the probability that C: the product of the numbers is even?
I know how to do it the long way, but there should be a simple way to do it: the answer is:
P(C)= 1-P(O,O)= 3/4
Could anyone explain what that means? Thanks.
Assuming the conditions described in first paragraph don't matter.
Now, C is the event of getting an even product. When is product of two numbers even? When either of the numbers (or both!) is even. i.e. the only case when the product is not even is when both of the numbers is odd.
Now, the hint says: $P(C) = 1 - P(O, O)$.
Here, $P(O, O)$ means that numbers on both dice (or on both throws of a single die, whatever), are odd; the event which is easier to calculate.
$P(O, O) = $ Number of first die is odd AND Number on second die is odd.
Since the dice throws are independent, $P(O, O) = P(\text{Getting odd number on first die)} \cdot P(\text{Getting odd number on second die}) = \_\_ \times \_\_ = \_\_$.
Since, it is the complement of this event that we are interested in, we subtract $P(O, O)$ from 1, to get $P(C)$. Thus, $P(C) = 1- P(O, O) = 1 - \_\_ = \_\_$
Now, can you fill the blanks in the above lines to get the desired answer?