Higher November 2018 Paper 4 Q22
22 In a village the ratio of males to females is 2 : 1.
40% of the people in the village are right-handed males.
25% of the people in the village are right-handed females.
Show that the proportion of females who are right-handed is greater than the proportion of males who are right-handed. [6]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
accept any correct method e.g. | B1 | Could be table or the correct probability notation e.g. P(R \(\cap\) M) = P(R/M) × P(M) | If they use a table see appendix based on 100 Award B3 for all five credited elements in table correct (see appendix), B2 for 3 or 4 correct, B1 for 2 correct M1 for Prop.(F) = 25 ÷ 33.333 or 0.75 M1 for Prop.(M) = 40 ÷ 66.666 or 0.6 |
| \(\frac{2}{3}\) × P(R/M) = \(\frac{2}{5}\) P(R/M) = \(\frac{2}{5} \div \frac{2}{3} = \frac{3}{5}\) | M1 M1 | Correct method to find the probability that a male is right-handed | |
| \(\frac{1}{3}\) × P(R/F) = \(\frac{1}{4}\) P(R/F) = \(\frac{1}{4} \div \frac{1}{3} = \frac{3}{4}\) | M1 M1 | Correct method to find the probability that a female is right-handed | |
| \(\frac{3}{4} = 0.75 \gt \frac{3}{5} = 0.6\) | A1 | Must be two figures which can be compared | |
Appendix: Q22 tables
Q22 tables based on 100 and 300 (the elements credited by B3, shown in red in the original, are the M and F entries of the R row and the M, F and Total entries of the Total row: 40, 25, 66.6[6..], 33.3[3..], 100 and 120, 75, 200, 100, 300)
| M | F | Total | |
|---|---|---|---|
| R | 40 | 25 | 65 |
| L | 26.6[6..] | 8.3[3..] | 35 |
| Total | 66.6[6..] | 33.3[3..] | 100 |
Accept 26.7 and 66.7
| M | F | Total | |
|---|---|---|---|
| R | 120 | 75 | 195 |
| L | 80 | 25 | 105 |
| Total | 200 | 100 | 300 |