Question 1
Paper 2Medium6 marksTwo independent fair spinners are used in a game. Spinner has four equally likely results, and spinner has five equally likely results, The outcome of a round is the ordered pair The table shows the sum for each possible outcome.
| 1 | 2 | 3 | 4 | 5 | |
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 |
| 2 | 3 | 4 | 5 | 6 | 7 |
| 3 | 4 | 5 | 6 | 7 | 8 |
| 4 | 5 | 6 | 7 | 8 | 9 |
Let be the event that the sum is at least 7.
(a)[2]
Find the theoretical probability of
(b)[1]
Find the probability of the complementary event
(c)[1]
Find the expected number of rounds in which occurs in 80 rounds.
(d)[1]
In a trial of 80 rounds, occurs 21 times. Find the relative frequency of
(e)[1]
Does this trial prove that the spinners are not fair? Give a reason.