1. 10B Discrete Random Variables Which of the following represent discrete random variables? the number of goals in a football match the height of students in this class shoe sizes number of girls in a family the time taken, in minutes, to run 10 kilometres.

2. 10B Discrete Random Variables – discrete probability distributions Let X represent the number of tails obtained in three tosses of a coin. Draw up a table that displays the values the discrete random variables can assume and the corresponding probabilities. throw 2 throw 1 throw 3 HHH HHT HTH HTT THH THT TTH TTT Head Tail Head Head Head Head Tail Tail Tail Head Tail Tail Head Tail

3. 10B Discrete Random Variables – discrete probability distributions properties All probabilities lie between 0 and 1 All of the probabilities add up to 1

4. 10B Discrete Random Variables – discrete probability distributions Let X represent the number of tails obtained in three tosses of a coin. Draw up a table that displays the values the discrete random variables can assume and the corresponding probabilities. Draw a probability distribution graph of these outcomes

5. 10B Discrete Random Variables Which of the following represent a discrete probability distribution?

6. 10B Discrete Random Variables Find the value of k for each of the following discrete probability distributions.

7. 10B Discrete Random Variables Find the value of k for each of the following discrete probability distributions.

8. 10B Discrete Random Variables Show that the function , where x = 2,3,4,5 is a probability function

9. 10B Discrete Random Variables Three balls are selected from a box containing 6 blue and 4 yellow balls. If the ball chosen after each selection is replaced before the next selection, find: a. the probability distribution for the number of blue balls drawn: i) 0 blue balls ii)1 blue ball iii) 2 blue balls iv) 3 blue balls the probability that 3 blue balls are chose given that at least one ball was blue. Probability BBB BBY BYB BYY YYY YYB YBY YBB

10. 10B Discrete Random Variables • Three balls are selected from a box containing 6 blue and 4 yellow balls. If the ball chosen after each selection is replaced before the next selection, find: • a. the probability distribution for the number of blue balls drawn: • i) 0 blue balls ii)1 blue ball iii) 2 blue balls iv) 3 blue balls • the probability that 3 blue balls are chose given that at least one ball was blue.