Probability is expressed as
number of favourable outcomes/number of total outcomes
If two events, A and B are mutually exclusive, they cannot occur together. Thus,
A or B = P(A) + P(B)
If two events, A and B are not mutually exclusive, they can both occur together. Thus,
A or B = P(A) + P(B) - P(A and B)
1) let the event of the spinner landing on an odd number be A. There are 4 odd numbers out of 8. Thus, probability of getting an odd number is
P(A) = 4/8
let the event of the spinner landing on a blue space be B. There are 3 numbers out of 8 in the blue space. Thus, probability of getting a number in the blue space is
P(B) = 3/8
We can see that both events are not mutually exclusive because the outcome of 5 out of 8 is common to both events. This probability is P(A and B) = 1/8
Thus, the probability of the spinner landing on an odd number or a blue space is
P(A) + P(B) - P(A and B) = 4/8 + 3/8 - 1/8
= 6/8
= 3/4
2) let the event of the spinner landing on a muliple of 3 be A. There are 2 multiples of 3 out of 8 possibilities. Thus, probability of getting a multiple of 3 is
P(A) = 2/8 = 1/4
let the event of the spinner landing on a purple space be B. There are 2 numbers in the purple space out of 8 possibilities. Thus, probability of getting a number in the purple space is
P(B) = 2/8 = 1/4
The events cannot occur together. Thus, they are mutually exclusive. Therefore, the probability of the spinner landing on an multiple of 3 or a purple space is
P(A) + P(B) = 1/4 + 1/4
= 1/2
