Higher November 2016 Unit 1 Q18
18. A game played at a children’s party involves throwing a ball into a bucket.
Each child tries to get the ball into the bucket in the least number of throws.
On each attempt, the probability that Sofia gets the ball into the bucket is 0·8.
Each attempt is independent of any previous attempt.
Show that she is 5 times more likely to get the ball into the bucket on her first attempt than to have her first successful throw on her second attempt.
You must show all your working. [3]
| Scheme | Marks | Comments |
|---|---|---|
| (Probability success at 1st attempt = 0·8) | ||
| (Probability 1st success at 2nd attempt =) 0·2 × 0·8 | M1 | Must show 0·2 × 0·8 for M1. |
| = 0·16 | A1 | |
| Convincing statement that 0·8 = 5 × 0·16 | A1 | A convincing statement must refer to 0·8 and 0·16 |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Probability 1st success at 2nd attempt =) 0·2 × 0·8 | M1 | |
| Indicates that this is 1/5th of probability of success at 1st attempt. | A1 | |
| So 5 times more likely to succeed 1st time. | A1 | |
| (Only convincing if 0·2 stated to be 1/5) |
Corrected by Westie's Workshop
- The board's mark scheme printed “‘So 5 times more likely to succeed 1st time.”. Changed to “So 5 times more likely to succeed 1st time.” because the opening quotation mark is never closed, so it is a stray character.
Original: see the board's mark scheme PDF (link above).