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Combined Events Statistics and Probability

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Finding all possible outcomes of two events Two coins are thrown. What is the probability of getting two heads? Before we can work out the probability of getting two heads we need to work out the total number of equally likely outcomes. There are three ways to do this: 1) We can list them systematically. Using H for heads and T for tails, the possible outcomes are: TH and HT are separate equally likely outcomes. HH.TT,TH,HT,

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Finding all possible outcomes of two events 2) We can use a two-way table. Second coin HT H T First coin HHHT THTT From the table we see that there are four possible outcomes one of which is two heads so, P(HH) = 1 4

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Finding the sample space A red dice and a blue dice are thrown and their scores are added together. What is the probability of getting a total of 8 from both dice? There are several ways to get a total of 8 by adding the scores from two dice. We could get a 2 and a 6,a 3 and a 5,a 4 and a 4, a 5 and a 3,and a 6 and a 2. To find the set of all possible outcomes, the sample space, we can use a two-way table.

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Finding the sample space + 234567 345678 456789 5678910 6789 11 789101112 From the sample space we can see that there are 36 possible outcomes when two dice are thrown. Five of these have a total of 8. 888 88 P(8) = 5 36

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96 5 4 83 2 31 654321+ Second die First die Sample space diagrams This table is another way of displaying all the outcomes from throwing two dice and adding them together. It is called a sample space diagram. Fill in the rest of the cells in the table. Colour in all the twos one colour, the threes another colour etc. What patterns do you notice in the table?

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1)What is the probability of getting a total more than 5? 2)What is the probability of getting a total less than 10? 3)What is the probability of getting a total that is a square number? 4)What is the probability of getting an even total? 5)What is the probability of getting an odd total? 6)What is the probability of getting a total less than 13? Sample space diagrams 1211109876 111098765 987654 9876543 8765432 7654321 654321+ Second die First die 121110987 11109876 98765 987654 876543 765432

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A coin and a ten-sided die are thrown and the outcomes recorded in the two-way table below. +12345678910 H2,H7,H T8,T Dice Coin Combined events with coins and dice Complete the table to show all the possible outcomes.

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1)How many outcomes are there? 2)What is the probability of getting a head and an even number? 3)What is the probability of getting a tail and a square number? Combined events +12345678910 H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H T1,T2,T3,T4,T5,T6,T7,T8,T9,T10,T Die Coin

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Two four-sided dice are thrown and the numbers added together. What is the probability of getting: 1)a total more than 4? 2)a total less than 8? 3)a prime number total? 4)a total that is at least 3? 5)a total of 4 or 5? 6)the same number on both dice? 7)a lower number on the first dice? 87654 76543 65432 54321 4321+ Second die First die Other combined events Construct a sample space diagram to show all the outcomes.

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Calculating the number of outcomes

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