On Mondays, Rani cooks her evening meal. She has a pizza, a burger or a curry with probabilities $$$0.35,0.44,0.21$$$ respectively. When she cooks a pizza, Rani has some fruit with probability $$$0.3$$$. When she cooks a burger, she has some fruit with probability $$$0.8$$$. When she cooks a curry, she never has any fruit. Find the probability that Rani does not have a burger given that she does not have any fruit. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_51 Year：2020 Question No：5(c)

Answer:

$\mathrm{P}($ not $\mathrm{B} \mid$ not fruit $)=\frac{\mathrm{P}\left(\mathrm{B}^{\prime} \cap \mathrm{F}^{\prime}\right)}{\mathrm{P}\left(\mathrm{F}^{\prime}\right)}$
$\frac{0.35 \times 0.7+0.21 \times 1}{1-\text { their }(\mathbf{b})}$
$\frac{0.455}{0.543}$
(M1 for 1 - their (b) or summing three appropriate 2-factor probabilities, correct or consistent with their tree diagram as denominator)
$0.838$ or $\frac{455}{543}$

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