Mutually Exclusive Outcomes

Supposing you roll a dice. The possible outcomes, or events, are scores of 1, 2, 3, 4, 5 and 6. These are said to be mutually exclusive, meaning that if one happens, the others do not.

Outcomes of experiments are not always mutually exclusive. For example, if you draw a card from a pack, one outcome is that it might be a heart, and another is that it might be a king. These are not mutually exclusive, since you can have a card that is both a heart and a king.

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

If you have a set of outcomes that cover all possible results of your experiment, then they are said to be exhaustive. The scores 1, 2, 3, 4, 5, 6 obtained by rolling a die are exhaustive, since no other score is possible.

The breakfast menu at a works canteen is always one of four options. Some of these options are more likely to be on the menu than others. The table shows the options available on any day, together with three of the four probabilities.

a) Copy the table, and fill in the value of the missing probability. b) Find the probability that the breakfast available on a randomly chosen day is: (i) cereal (ii) sausages or bacon & eggs (iii) not fish fingers.

A biased dice shows scores of 1, 2, 3, 4, 5, 6 with these probabilities:

The dice is rolled once. Find the probability that the score obtained is:

a) 5 b) not 2 c) 3 or 4 d) an even number.

Alexei has a tin of crayons. Each crayon is either red or blue or yellow or green. The number of yellow crayons is the same as the number of green crayons.

Alexei chooses a crayon at random from the tin. The probability that he chooses a red crayon is 0.3. The probability he chooses a blue crayon is 0.4.

a) Find the probability that the crayon is red or blue. b) Find the probability that the crayon is yellow or green. c) Find the probability that the crayon is green.

A bag contains red, green, blue and yellow counters. In a probability experiment, one counter is chosen at random and removed from the bag. Its colour is noted, and it is returned to the bag. The table shows some probabilities for this experiment:

a) Find the probability of obtaining a yellow counter. b) The experiment is carried out 250 times. Estimate the number of times a blue counter is obtained. c) Rewrite the probability table to show the probabilities as fractions with the same denominator. d) Altogether, the bag contains n counters. What is the lowest possible value of n?