Respuesta :
Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.
The expected value is given by the sum of each outcome multiplied by it's respective probability.
In this problem:
- The player wins $6, that is, Ayo loses £6, if he rolls a 6 and spins a 1, hence the probability is [tex]\frac{1}{6} \times \frac{1}{12} = \frac{1}{72}[/tex].
- The player wins $3, that is, Ayo loses £3, if he rolls a 3 on at least one of the spinner or the dice, hence, considering three cases(both and either the spinner of the dice), the probability is [tex]\frac{1}{6} \times \frac{1}{12} + \frac{1}{6} \times \frac{11}{12} + \frac{5}{6} \times \frac{1}{12} = \frac{1 + 11 + 5}{72} = \frac{17}{72}[/tex]
- In the other cases, Ayo wins £1.40, with [tex]1 - \frac{18}{72} = \frac{54}{72}[/tex] probability.
Hence, his expected profit for a single game is:
[tex]E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583[/tex]
For 216 games, the expected value is:
[tex]E = 216(0.2583) = 55.8[/tex]
Ayo can be expected to make a profit of £55.8.
To learn more about expected value, you can take a look at https://brainly.com/question/24855677
