Foundation November 2023 Paper 2 Q13
13.
(a)
Three fair coins are thrown at the same time.
(i)
Complete the table to list all the different possible outcomes.
The first row has been completed for you. [2]
| Coin 1 | Coin 2 | Coin 3 |
|---|---|---|
| H | H | H |
You may not need all the lines in the table.
(ii) Write down the probability that the outcome is three heads. [1]
(b)
When four fair coins are thrown at the same time, the probability that the outcome is two heads and two tails is 0·375.
If the same four coins are thrown 136 times, how many times would you expect to get the outcome two heads and two tails? [2]
| Scheme | Marks | Comments | |||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
(i)
| B2 | For a fully correct table. Allow HHH to be repeated but no others. B1 for at least five different outcomes. | |||||||||||||||||||||||||||
| (ii) \(\frac{1}{8}\) oe | B1 | FT \(\dfrac{1}{\text{‘their total number of outcomes’}}\), provided B1 previously awarded. Note: 3/24 is awarded B0 (from counting H and T’s in the table) |
| Scheme | Marks | Comments |
|---|---|---|
| 0.375 × 136 oe | M1 | |
| = 51 (times) | A1 | Note: Answer of 51/136 is awarded M1 A0 If no marks, award SC1 for an answer of 85 (from 0.625 × 136) |
| (5) |