The probability that our school will host soccer and rugby tournament this year is 0.8. If we host the the probability of winning soccer is 0.7. if we do not host the probability of winning soccer is 0.4. if we win soccer the probability of winning rugby is 0.8, otherwise if we lose soccer the probability of winning rugby is 0.3.

a)draw a tree diagram to represent this information.
b)use the tree diagram to find:-
i) the probability that we will lose both games.
ii) the probability that we will win only one game.
iii) the probability that we will host and lose both games.

3 answers

first branch:
host (h) = .8
not host (nh) = .2

second level:
h, win soccer(ws) = .7
h, lose soccer(ls) = .3
nh, ws = .4
nh, ls = .6

third level:
h, ws, win rugby(wr) = .8
h, ws, lose rugby(lr) = .2
h, ls, wr = .3
h, ls, lr = .7
nh, ws, wr = .8
nh, ws, lr = .2
nh, ls, wr = .3
nh, ls, lr = .7

lose both games: h,ls, lr + nh, ls, lr
= (.8)(.3)(.7) + (.2)(.6)(.7)
= .168 + .084
= .252

follow the paths in your tree to answer the other two questions

(btw, I tested my tree, the prob of all 8 end points add up to 1)

It is hard do it for me