CONDITIONAL PROBABILITY: MUTUALLY EXCLUSIVE EVENTS

Events are mutually exclusive if they cannot happen at the same time. For example, if we toss a coin, either heads or tails might turn up, but not heads and tails at the same time. Similarly, in a single throw of a die, we can only have one number shown at the top face. The numbers on the face are mutually exclusive events.

If A and B are mutually exclusive events then the probability of A happening OR the probability of B happening is P(A) + P(B).

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

Example:

What is the probability of a die showing a 2 or a 5?

Solution:

Example:

The probabilities of three teams A, B and C winning a badminton competition are

Calculate the probability that

a) either A or B will win

b) either A or B or C will win

c) none of these teams will win

d) neither A nor B will win

Solution:

c) P(none will win) = 1 – P(A or B or C will win)

d) P(neither A nor B will win) = 1 – P(either A or B will win)

CONDITIONAL PROBABILITY: INDEPENDENT EVENTS

Events are independent if the outcome of one event does not affect the outcome of another. For example, if you throw a die and a coin, the number on the die does not affect whether the result you get on the coin.

If A and B are independent events, then the probability of A happening AND the probability of B happening is P(A) × P(B).

P(A and B) = P(A) × P(B)

Example:

If a dice is thrown twice, find the probability of getting two 5’s.

Solution:

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