Question

2. How do you find P(A or B) if A and B are independent events for one action, such as spinning a four-color spinner once and finding P(red or blue)?

Answer 1

P(red or blue) =
`(7)/(16)`.

Explanation:

We have to find P(A or B), if A and B are independent events for one action, such as spinning a four-color spinner once.

Firstly, as we know that the formula for finding P(A or B) is given by;

P(A or B) = P(A) + P(B) - P(A and B)

Since it is stated that event A and B are independent, this means that there is no dependence of any one event on another event, so;

P(A and B) = P(A)
`*` P(B)

Now, we can find P(A or B) = P(A) + P(B) - P(A)
`*` P(B); is we know that the probabilities of happening of both events.

Similarly, P(red or blue) = P(red) + P(blue) - P(red)
`*` P(blue).

Since the event is spinning a four-color spinner once and assuming there are four different colors, so the probability of wheel stopping on each color is (
`(1)/(4)`).

So, P(red or blue) =
`(1)/(4) +(1)/(4) -((1)/(4) * (1)/(4) )`

=
`(2)/(4) -(1)/(16)` =
`(7)/(16)`.