Question

Roll a die: Get a prime number or get an even number

Answer 1

Two events are mutually exclusive if they cannot occur at the same time, which means mutually exclusive is disjoint, If two events are disjoint, then the probability of them both occurring at the same time is 0.

1. In this case, for Getting a prime number or get an even number:

`P(P\text{ }\cap\text{ E)=0}`

Because we cannot roll an even number or a prime number at the same time, so they are mutually exclusive.

2. For selecting a female doctor or the doctor who has blue eyes:

`P(F\cup B)`

It can happen at the same time, then they are NOT mutually exclusive.

3. For getting a heart or a black card:

`P(H\cap B)=0`

Because we cannot get a heart (red card) or a black card at the same time, they are mutually exclusive.

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