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 $$$0.3$$$. Find the probability that on a randomly chosen day Georgie wears a yellow scarf given that she does not wear a hat. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_m21_qp_52 Year：2021 Question No：2(b)

Answer:

$P(Y \mid \bar{H})=\frac{P(Y \cap \bar{H})}{P(\bar{H})}=\frac{0.35 \times 0.7}{1-\text { their }(\mathbf{a})}=\frac{0.245}{0.515}$
$0.476$ or $\frac{49}{103}$

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