guide 5 probability pg 119, check your skills q3

[kpatel986]

Please explain

A fair die is rolled and a fair coin is flipped. What is the probability that either the die will come up 2 or 3, or the coin will land heads up?

my answer: P (2 or 3) or P(1 head)= (1/6 + 1/6) + (1/2) = 5/6

this is an " or probability" question

can you also explain the term "mutually exclusive" ?

[tommywallach]

Hey Kpatel,

Think about the logic this way. If I flip three coins, what are the odds that the first one will come up odd, the second will come up even, or the third will come up odd.

By your logic, the answer would be 1/2 + 1/2 + 1/2. But of course, that isn't possible, because the probability would be greater than 1.

In this situation, you need to remember that there are three situations that could make us happy here:

1. Die success and coin failure
2. Die failure and coin success
3. Die success and coin success

1. 1/3 * 1/2 = 1/6
2. 2/3 * 1/2 = 2/6
3. 1/3 * 1/2 = 1/6

Answer is 4/6 --> 2/3

Mutually exclusive simply means that the two events have no connection to each other (rolling the die has no effect on the coin).

You could also do this question with the 1-x trick. The only thing that WOULD NOT be good (i.e. unsuccessful outcome) here would be:

Die failure and coin failure

2/3 * 1/2 = 1/3

Then we just do 1 - 1/3 = 2/3 to get the answer.

-t