Question

The probablity that Mr. Brow completes a cross word puzzle is 2/3 than Mr.Black complete it is 1/2 and that Mr.White complete it is 1/3.

Find the probability that

(a). All three complete it
(b) at least one of them complete it.

Answer 1

that*

Answer 2

a) 1/9
b) 1/9

Answer 3

b) 8/9 sorry

Answer 4

oh the working?

Answer 5

P(1) = probability of Mr. Brow solving it=2/3
P(2)= probability of Mr. Black solving it=1/2
P(3)= probability of Mr. white solving it=1/3
a) All three complete it
P= P(1)P(2)P(3)
\[P=\frac{2}{3} \times \frac{1}{2} \times \frac{1}{3}=\frac{2}{18}= \frac{1}{9}\]

Answer 6

b) Atleast one of them complete it
P= 1-P( none of them complete)
P(1') = probability of Mr. Brow not solving it=1-2/3=1/3
P(2')= probability of Mr. Black not solving it=1-1/2=1/2
P(3')= probability of Mr. white not solving it=1-1/3=2/3
\[P= 1- (\frac{1}{3} \times \frac{1}{2}\times \frac{2}{3})=1-\frac{2}{18}=1-\frac{1}{9}=\frac{8}{9}\]

Answer 7

For part b it asks for at least 1 of them completing so we can either find the probabilities that exactly 1, exactly 2, and exactly 3 of them complete it and add them together, or we can find the probability that none of them complete it and subtract it from 1, which is much quicker. probability that none complete it is Mr Brown 1/3 times mr white 2/3 times mr black 1/2 = 1/9, 1 - 1/9 = 8/9