Answer:
The Probabilty distribution for the amount Godfrey gains in one turn is then given as
X ||| P(X)
15p | 0.0278
5p | 0.278
-5p | 0.6942
Step-by-step explanation:
If random variable X represents the amount Godfrey gains in one turn.
There are 3 different possible outcomes for X.
- Godfrey pays 5p to enter the game and gets two sixes and wins 20p.
Net gain = 15p
Probability of getting two sixes from two fair dice
= (number of outcomes with two sixes) ÷ (total number of outcomes)
number of outcomes with two sixes = 1
total number of possible outcomes = 36
Probability of getting two sides from two fair dice = (1/36) = 0.0278
- Godfrey pays 5p to enter the game and gets only one six and wins 10p.
Net gain = 5p
Probability of getting one six from either of two fair dice
= (number of outcomes with one six) ÷ (total number of outcomes)
number of outcomes with one six = 2 × n[(6,1), (6,2), (6,3), (6,4), (6,5)] = 2 × 5 = 10
total number of possible outcomes = 36
Probability of getting two sides from two fair dice = (10/36) = 0.278
- Godfrey pays 5p to enter the game and doesn't win anything
Net gain = -5p
Probability of not getting two sixes or one six.
= 1 - [(Probability of getting two sixes) + (Probability of getting one six on.wither dice)]
= 1 - 0.0278 - 0.278 = 0.6942
Probability of getting not getting two sixes or one six = 0.6942
The Probabilty distribution for the amount Godfrey gains in one turn is then given as
X ||| P(X)
15p | 0.0278
5p | 0.278
-5p | 0.6942
Hope this Helps!!!
