Grade DE Mutually exclusive events Know that the

Grade D/E Mutually exclusive events Know that the sum of all possible mutually exclusive outcomes is 1. If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key Vocabulary Mutually exclusive Event Exhaustive

Mutually exclusive If two events are mutually exclusive, the can’t both happen. Examples: • If someone is a man, they can’t be a woman • If you win a game, you can’t lose it at the same time. • If you throw a die and get a five, you can’t get a four at the same time.

Examples of events which are NOT mutually exclusive • If you are a man you may also be under the age of 21. • If you throw an even number, you may also have thrown a six. • If you draw a rectangle, it may also be a square.

Exhaustive events cover all possible outcomes. Examples • Throwing a die – you either get a six or you don’t • Tossing a coin – you get a Tail or a Head • Playing a game of football – you win, lose or draw. If events are mutually exclusive and exhaustive, their probabilities add up to 1.

Examples 1. If the probability of catching flu in winter is 0. 7, what is the probability of not catching flu? 2. Tom plants some seeds. They are all of one type of plant, but are three different colours. The probability of any individual plant being red is 0. 38 and blue 0. 43. The third colour is white. What is the probability of a randomly chosen plant being white? 3. The probability of record rainfall next winter is 0. 6. What is the probability of rainfall not being a record?

Solutions to examples 1. If the probability of catching flu in winter is 0. 7, what is the probability of not catching flu? 1 – 0. 7 = 0. 3 2. Tom plants some seeds. They are all of one type of plant, but are three different colours. The probability of any individual plant being red is 0. 38 and blue 0. 43. The third colour is white. What is the probability of a randomly chosen plant being white? 1 – 0. 38 – 0. 43 = 0. 19 3. The probability of record rainfall next winter is 0. 6. What is the probability of rainfall not being a record? 1 – 0. 6 = 0. 4

Now try these 1. The probability of John scoring a hat-trick is 0. 3. What is the probability of John not scoring a hat trick? 2. In tennis, you can win a set outright, lose it outright or see it go to a tie-break. From an analysis of past games, the chances of Andy winning a set of tennis outright is 0. 6 and the chances of losing outright is 0. 25. What is the probability of seeing it go to a tie-break?

Solutions 1. The probability of John scoring a hat-trick is 0. 3. What is the probability of John not scoring a hat trick? 1 – 0. 3 = 0. 7 2. In tennis, you can win a set outright, lose it outright or see it go to a tie-break. From an analysis of past games, the chances of Andy winning a set of tennis outright is 0. 6 and the chances of losing outright is 0. 25. What is the probability of seeing it go to a tie-break? 1 – 0. 6 – 0. 25 = 0. 15

Problem Solving and Reasoning A game involves throwing a die. The die is not a fair die (it is biased – some numbers are more likely to come up than others). The probabilities are given in the table below. Find the missing probabilities. Number on die Probability 1 2 3 4 5 6 0. 1 x 0. 2 3 x 0. 3

Problem Solving and Reasoning A game involves throwing a die. The die is not a fair die (it is biased – some numbers are more likely to come up than others). The probabilities are given in the table below. Find the missing probabilities. Number on die Probability 1 2 3 4 5 6 0. 1 x 0. 2 3 x 0. 3 Form an equation 1 = 0. 1 + x + 0. 2 + 3 x + 0. 3 Solve 0. 2 = 4 x x = 0. 05 Hence p(2) = 0. 05 and p(5) = 0. 15

Try this……. . A bag contains balls that are blue, orange or green. Colour Blue Orange Green Probability 0. 3 2 x x + 0. 1 A counter is chosen at random. Work out the probability it is orange and the probability it is green.

Try this……. . A bag contains balls that are blue, orange or green. Colour Blue Orange Green Probability 0. 3 2 x x + 0. 1 A counter is chosen at random. Work out the probability it is orange and the probability it is green. Form an equation 1 = 0. 3 + 2 x + 0. 1 Solve the equation 0. 6 = 3 x x = 0. 2 Hence p(orange) = 0. 4 and p(green) = 0. 3