Foundation November 2018 Paper 2 Q18
18. A biased dice has been used for an experiment.
The probabilities of 1, 2, 3 and 6 occurring on any throw of the dice are shown in the table below.
| Number on dice | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Probability | 0·1 | 0·17 | 0·24 | 0·25 |
The probability of throwing a 4 is the same as the probability of throwing a 5.
(a) Complete the table. [3]
(b) The dice is thrown once. Calculate the probability of throwing a number less than 4. [1]
(c) The dice is thrown 600 times.
Show that a 2 is expected to occur more than 100 times. [2]
Show that a 2 is expected to occur more than 100 times. [2]
| Scheme | Marks | Comments |
|---|---|---|
| 1 − [0.1 + 0.17 + 0.24 + 0.25] (= 0.24) | M1 | Mark correct responses completed into the table. |
| ÷ 2 | m1 | |
| Table completed with 0.12 and 0.12 | A1 | CAO |
| Scheme | Marks | Comments |
|---|---|---|
| 0.51 | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| 600 x 0.17 | B1 | Alternative: 1/6 = 0.166(…) < 0.17 B1 1/6 of 600 = 100, so Exp(2) > 100 B1 |
| = 102 | B1 | |
| (6) |