Download Strand 1

Leaving Certificate Mathematics - Strand 1 - STATISTICS AND PROBABILITY
Q. 3
A roulette wheel has 38 numbers; 18 black, 18 red and 2 green
a. Game1: Bet on a Number
Bet €1 on a number; if you are right you win €35 (and you get your €1 back). The
outcome is +35 because you are ‘up’ €35. If you are wrong, you lose €1. What is your
outcome?
Is this a fair game?
b. Game 2: Bet On Black
Bet €1 on a black number
If right win €1 (and get your €1 stake back). If wrong, you lose €1.
What is the expected value? Is this a fair game?
The following example is more challenging, since it doesn’t refer to gaming.
Q. 4
Consider two family planning strategies.
(a) have children until you have a girl or (b) stop after two boys.
Would either strategy upset the male /female mix in the population? What do you think?
Make a prediction.
If you calculate the expected value or mean number of boys for a large population
of families and compare this with the expected value or mean number of girls for a
large population of families you will be able to answer this question.
Discuss in your group why this information will help you decide if either strategy would
upset the male/female mix.
Use probability trees to help find the probability of each outcome. Think about the possible
outcomes
Girl first (what happens now?); Boy, Girl (what happens now?); Boy, Boy (what happens now?)
What’s the average number of boys per family? Complete the probability column in the table
below.
Now look at the definition of expected value again and see if you can calculate the expected
value or the average number of boys per family. Can you complete the final column in the table?
Boys
Probability
Value × Probability
0
1
2
53
NCCA Proj Maths LC S1 V2.indd 53
13/11/2009 09:13