A-LevelMathematicsProbability and statistics9709/52 · Feb/Mar 2021 · Q25 Marks
Georgie has a red scarf, a blue scarf and a yellow scarf. Each day she wears exactly one of these scarves. The probabilities for the three colours are 0.2, 0.45 and 0.35 respectively. When she wears a red scarf, she always wears a hat. When she wears a blue scarf, she wears a hat with probability 0.4. When she wears a yellow scarf, she wears a hat with probability 0.3.
- (a)Find the probability that on a randomly chosen day Georgie wears a hat.[2]
- (b)Find the probability that on a randomly chosen day Georgie wears a yellow scarf given that she does not wear a hat.[3]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2021). The mark or mark type is shown in brackets.
- [1] M1 0.2 [×1] + 0.45 × b + 0·35 × c, b = 0.4, 0.6 c = 0.3, 0.7
- [1] A1
- [1] B1 0.35 × 0.7 or 0.245 seen as numerator or denominator of fraction.
- [1] M1 0.515 or 1 – their (a) or [0.3 × 0+] 0.45 × d + 0·35 × e, where d = their b', e = their c' seen as denominator of fraction.
- [1] A1 0.4757 < p < 0·476
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