Mutually Exclusive Probability

Objective: I know how to find the probability events that are mutually exclusive..

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).

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Work out the following.

When necessary, give your answer in fractions eg. 2/5

1. If an unbiased die is thrown, what is the probability that it will show a 3 or an even number?

2. A box contains 20 red, 10 blue and 30 yellow beads. What is the probability of a bead drawn at random being:
a) red or blue?

b) yellow or blue?

c) red, blue or yellow?

3. Two fair dice, one coloured red and one coloured blue, are thrown. Calculate the probability that:
a) the score on the red die is 4.

b) either die shows a score of 6.

c) the score on the blue die is either 3 or 5.

d) the score on the red die is neither 1 nor 2.

e) either die shows a 4 or 5.

f) neither die shows a 3 or 6.

4. The letters of the words ‘HELLO’ and ‘THERE’ are written on individual cards and the cards placed into a bag. A card is picked at random. What is the probability of picking:
a) the letter ‘L’

b) the letter ‘E’

c) the letter ‘L’ or ‘E’

d) a consonant

e) the letter ‘E’ or a consonant

f) the letter ‘L’, ‘E’ or ‘T’

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