Higher November 2018 Paper 3 Q16
16 In a running club there are 50 females and 80 males.
If a female is chosen at random, the probability she has blue eyes is 0.38
If a male is chosen at random, the probability he has blue eyes is 0.6
One person is chosen at random.
Show that the probability the person has blue eyes is more than 0.5 [4 marks]
| Answer | Mark | Comments |
|---|---|---|
| Alternative method 1 | ||
| \(0.38 \times 50\) or 19 | M1 | oe |
| \(0.6 \times 80\) or 48 | M1 | oe |
| \(\dfrac{\text{their } 19 + \text{their } 48}{50 + 80}\) or \(\dfrac{67}{130}\) | M1dep | oe |
| 0.51(5…) or 0.52 or \(\dfrac{67}{130}\) and \((67 \times 2 =)\ 134\) or \(\dfrac{67}{130}\) and \((130 \div 2 =)\ 65\) | A1 | oe |
| Alternative method 2 | ||
| \(0.38 \times 50\) or 19 | M1 | oe |
| \(0.6 \times 80\) or 48 | M1 | oe |
| \(0.5 \times (50 + 80)\) or 65 | M1dep | oe |
| 65 and 67 | A1 | |
| Alternative method 3 | ||
| \(0.38 \times 50\) or 19 | M1 | oe |
| \(0.5 \times (50 + 80)\) or 65 | M1 | oe |
| \(\dfrac{\text{their } 65 - \text{their } 19}{80}\) or \(\dfrac{46}{80}\) | M1dep | oe |
| 0.575 | A1 | |
| Alternative method 4 | ||
| \(0.6 \times 80\) or 48 | M1 | oe |
| \(0.5 \times (50 + 80)\) or 65 | M1 | oe |
| \(\dfrac{\text{their } 65 - \text{their } 48}{50}\) or \(\dfrac{17}{50}\) | M1dep | oe |
| 0.34 | A1 | |
| Alternative method 5 | ||
| \(\dfrac{50}{130} \times 0.38\) or 0.14… or 0.15 | M1 | oe |
| \(\dfrac{80}{130} \times 0.6\) or 0.36… or 0.37 | M1 | oe |
| \(\text{their } 0.14… + \text{their } 0.36…\) | M1dep | oe |
| 0.51(5…) or 0.52 | A1 | |