Question #5217

Q3. An urn contains 7 balls, 4 of which are black and the rest white.
(a) Two are drawn together and one is found to be black. What is the probability that the other is also?
[5 marks]
(b) Starting with all 7 balls in the urn, balls are drawn randomly without replacement until all 3 white balls are found. What is the probability that the third white ball is found on the
(i) fourth attempt? (ii) seventh attempt?
[10 marks]

Expert's answer

(a) & there are 3 black balls left

And also 3 white

So p(ball=black)=3/6=0.5

(b) (i) & w-we pick white ball

b- black/

white ball is found on the fourth attempt& so there can be combinations

wwbw p=3/7*2/6*4/5*1/4=1/35

wbww& p=3/7*4/6*2/5*1/4=1/35

bwww p=4/7*3/6*2/5*1/4=1/35

P=3/35

(ii)

The prob. Is absolutely the same as if we pick the last ball,and it should be white

P(ball=white)=3/7

And also 3 white

So p(ball=black)=3/6=0.5

(b) (i) & w-we pick white ball

b- black/

white ball is found on the fourth attempt& so there can be combinations

wwbw p=3/7*2/6*4/5*1/4=1/35

wbww& p=3/7*4/6*2/5*1/4=1/35

bwww p=4/7*3/6*2/5*1/4=1/35

P=3/35

(ii)

The prob. Is absolutely the same as if we pick the last ball,and it should be white

P(ball=white)=3/7

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