Thread: Probability of mutually exclusive events

1. Probability of mutually exclusive events

A four-faced dice is rolled.Given A is an event of obtaining an even number and B is an event of obtaining a number less than 3.

a)determine if event A and B are mutually exclusive

b)Find the probability of obtaining an odd number or the number 4.

2. Originally Posted by mastermin346
A four-faced dice is rolled.Given A is an event of obtaining an even number and B is an event of obtaining a number less than 3.

a)determine if event A and B are mutually exclusive

b)Find the probability of obtaining an odd number or the number 4.
Hi mastermin346,

(a)

If you calculate the probability of obtaining a number <3,
will you be including the probability that a "2" was rolled ?
Are these events "mutually exclusive" ?

(b)

Is 4 odd?

Hence if you calculate the probability of landing an odd number,
will that include the probability of obtaining a 4?
Are these events mutually exclusive?

Hence, what do we do with the probabilities of both events to calculate the overall probability of "odd" or "4" ?

3. If two events $\displaystyle A$ and $\displaystyle B$ are mutually exclusive then $\displaystyle Pr(A \cap B) = 0$ and

$\displaystyle Pr(A \cup B) = Pr(A) + Pr(B)$ (this follows from the Addition Rule).

Can you work out $\displaystyle Pr(\textrm{Even } \cup <3)$? Is this the same as $\displaystyle Pr(\textrm{Even}) + Pr(<3)$?