GCSE Revision Notes Mathematics Probability

Transcription

1 GCSE Revision Notes Mathematics Probability

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3 Probability The probability of an event is always between 0 and 1. 0 meaning there is a 0% chance the event will happen and 1 meaning there is a 100% chance the event will happen. Everytime you use the word or in probability terms it means you add the probabilities For example when rolling a dice what is the probability of getting 1 or 2? We see the word or so we know that we add our two probabilities + = Everytime you use word and in probability terms it means you multiply the probabilities Rolling two die what is the probability of getting a 1 and a 2? We see the word and so we know that we multiply our probabilities The probability of an event happening is The probability of an event not happening is 1 - This is because (The probability of an event happening) + (The probability of an event not happening) = 1 Because either an event occurs or it doesn t If you want to get the probability of something happening at least once we use the formula 1 - (probability that nothing happens)

4 Questions 5.1 In a cafe, a customer orders one drink. The probability that he orders tea is 0.42 The probability that he orders coffee is 0.3 Work out the probability that he orders either tea or coffee or so we add the probabilities = In a game, players try to win a coloured counter. There are six possible colours. The table shows the probability of winning each colour. Colour of counter Probability Yellow 0.04 Green 0.07 Brown 0.09 Blue 0.10 Pink 0.13 Black 0.14 (i)which colour is twice as likely to be won as green? Green = = 0.14 Black = 0.14 Black is twice as likely to be won as green (ii) Work out the probability of winning yellow or brown. Probability of winning yellow or brown = 0.13 (iii) Sam plays the game 160 times. Estimate the number of times that he does not win = = 0.43 of the time he does not win = 68.8 He doesn t win approximately 69 times

5 5.3 (i) A football strip consists of a shirt, shorts and socks. Aspen United has two shirts, blue and green, from which to select. They also can select from three different colours of shorts and five different colours of socks, including red in each case. Calculate how many different strips Aspen United can have? Each team must have a shirt, a pair of shorts and a pair of socks and so we multiply 2 shirts, 3 shorts, 5 socks = 30 (ii) Willow Celtic plays in an all red strip. When Aspen United plays Willow Celtic, Aspen United are not allowed to use their red shorts or their red socks. Calculate how many different strips Aspen United can have when they play Willow Celtic. One less pair of shorts and one less pair of socks available = A fair circular spinner consists of three equal sectors. Two are coloured blue and one is coloured red. The spinner is spun and a fair coin is tossed. (i) What is the probability of the spinner landing on a blue sector? 2 in 3 chance so (ii) Find the probability of getting a head and a red. and so we multiply (iii) Find the probability of getting a tail and a blue. =

6 5.5 Ten different names are put into a computer. One of the names is John. On Monday, the computer chooses two names at random. The computer is set so that the same name can be chosen twice. Show that the probability that John is chosen at least once is John can be picked on the first go or on the second go or twice John is picked on the first go and a different name is picked on the second go John is picked on the second go and a different name is picked on the first go John is picked both times + + = (ii) On Tuesday, the computer chooses two names at random. The computer is set so that the same name cannot be chosen twice. Work out the probability that John is chosen now John is picked on the first go and any name can then be picked or John is picked on the second go and a different name is picked first John is picked on the first go John is picked on the second go =

7 + = = 5.6 A bag contains only red counters and blue counters. There are 6 more red than blue. A counter is chosen at random from the bag. The probability it is blue is How many red counters are in the bag? x = number of blue counters x + 6 = number of red counters The probability a counter is blue is The bag contains 4x counters 4x - x = 3x red counters 3x = x + 6 2x = 6 x = 3 Number of red counters = x + 6 = A bag only contains black counters and white counters. A counter is chosen from the bag at random and replaced. Another counter is then chosen from the bag at random. The probability of choosing two black counters is 0.36 (i) Show that the probability of choosing a black counter each time is 0.6 The probability of choosing a black counter and another black counter = 0.36 Prob of black counter Prob of black counter = 0.36 Prob of black counter = 0.36 = 0.6 (ii) Work out the probability of choosing two white counters The probability of choosing a black counter = = 0.4 The probability of choosing a white counter and another white counter = 0.16 (iii) Work out the probability of choosing at least one white counter.

8 1 - (probability of choosing 2 black counters) = 0.64