- [Maximum mark: 7]
Gustav plays a game in which he first tosses an unbiased coin and then rolls an unbiased six-sided die.
If the coin shows tails, the score on the die is Gustav’s final number of points.
If the coin shows heads, one is added to the score on the die for Gustav’s final number of points.
(a) Find the probability that Gustav’s final number of points is 7. [2]
(b) Complete the following table. [3]
| Final number of points | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Probability |
(c) Calculate the expected value of Gustav’s final number of points. [2]