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Combined Events

Combined Events. Sample Space Diagrams. 1) We can list them systematically. TH and HT are separate equally likely outcomes. Two coins are thrown. What is the probability of getting two heads?.

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Combined Events

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  1. Combined Events Sample Space Diagrams

  2. 1) We can list them systematically. TH and HT are separate equally likely outcomes. 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. Finding all possible outcomes of two events There are three ways to do this: Using H for heads and T for tails, the possible outcomes are: TT, TH, HT, HH.

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

  4. A red dice and a blue dice are thrown and their scores are added together. Finding the sample space 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.

  5. 8 5 8 8 8 8 36 + From the sample space we can see that there are 36 possible outcomes when two dice are thrown. 2 3 4 5 6 7 Finding the sample space 3 4 5 6 7 8 Five of these have a total of 8. 4 5 6 7 8 9 5 6 7 8 9 10 P(8) = 6 7 8 9 10 11 7 8 9 10 11 12

  6. Second die + 1 2 3 4 5 6 1 3 2 3 8 First die 4 5 6 9 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?

  7. Second die + 1 2 3 4 5 6 1 2 3 4 5 6 7 2 3 4 5 6 7 8 3 4 5 6 7 8 9 First die 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12 Sample space diagrams • What is the probability of getting a total more than 5? • What is the probability of getting a total less than 10? • What is the probability of getting a total that is a square number? • What is the probability of getting an even total? • What is the probability of getting an odd total? • What is the probability of getting a total less than 13? 2 3 4 5 6 7 3 4 5 6 7 8 4 5 6 7 8 9 5 6 7 8 9 10 6 7 8 9 10 11 7 8 9 10 11 12

  8. Combined events with coins and dice A coin and a ten-sided die are thrown and the outcomes recorded in the two-way table below. Dice Coin Complete the table to show all the possible outcomes.

  9. Combined events Die Coin • How many outcomes are there? • What is the probability of getting a head and an even number? • What is the probability of getting a tail and a square number?

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

  11. Calculating the number of outcomes

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