Box $A$ contains $10$ red, $8$ blue and $7$ green balls. Box $B$ contains $2$ white and $3$ black ba

Question

Box $A$ contains $10$ red, $8$ blue and $7$ green balls. Box $B$ contains $2$ white and $3$ black balls. All the balls are indistinguishable except for their colours. Three balls are taken from Box $A$ and two balls are taken from Box $B$, at random and without replacement. Mr Wong guesses that there are at least $1$ red ball and exactly $2$ black balls taken, while Mr Tan guesses that all the balls taken are of different colours. Show that the probability that Mr Wong is correct is $0.241$, correct to $3$ significant figures. [3] Find the probability that Mr Tan is correct. [2] Find the probability that Mr Wong is correct, given that Mr Tan is wrong. [3]

Accepted Answer

(i) $\frac{1107}{4600}=0.241$ (3 s.f.) (ii) $\frac{84}{575}$ (iii) $\frac{1107}{3928}=0.282$ (3 s.f.)

2016 VJC P2 Q7

2016 VJC P2 Q7

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