Rules and Examples

The P(GG) can be written as P(G) and P(G). Use of the word 'and' indicates that we multiply the probabilities.

When the word 'or' can be used it indicates (+), so we add the probabilities.

Example 1: In a bag of green and blue discs, what is the probability of selecting 2 discs of different colours, if the first disc is returned before selecting the second.

Example 2: Twins Mary and John are taking a driving test. If the probability of Mary passing is 0.6 and the probability of John passing is 0.2, what is the probability of only one twin passing?

P(Mary fails) = 1 – 0.6 = 0.4 

P(John fails) = 1 – 0.2 = 0.8

Mutually Exclusive Events

P(A or B) = P(A) + P(B) can only be used when A and B are mutually exclusive events, i.e. they cannot happen together.

Example 1: Three cards are presented (4 of Clubs, 3 of Diamonds and 5 of Spades). If one is selected, what is the probability of getting a 4 or a Club?

We cannot say P(4 or Club) = P(4) + P(Club) because they can happen together. The 4 can also be a Club, so the events are not mutually exclusive.
 

Example 2: The probability that the weather is fine on Monday is 0.3.

If it is fine, the probability that I can get on my bus is 0.8. If it is not fine, the probability that I can get on my bus is 0.2.

Find the probability that I can get on my bus on Monday.

Example 3: When Jane goes shopping, the probability she travels by bus is 0.25, by taxi is 0.1 and on foot is 0.6. What is the probability that she returns (a) by bus or taxi, (b) by bus or on foot?

a) By bus or taxi