急! F5 Probability 05q1

15.
P(revise) = 0.2
P(not revise) = 1 - 0.2 = 0.8

Therefore, P(pass) = 0.2(0.85) + 0.8(0.65) = 0.69

18.
(a)
P(go straight at a junction) = 2/3
P(turn right at a junction) = 1 - 2/3 = 1/3
P(crash) = (1/3)(2/3)(2/3) = 4/27

(b)
P(enter depot)
= P(enter depot through B) + P(enter depot through C)
= (1/3)(1/3) + (1/3)(2/3)(1/3)
= 1/9 + 2/27
= 5/27

ALTERNATIVE WAY:
P(enter depot)
= 1 - P(not enter depot)
= 1 - [P(go straight at A) + P(crash)]
= 1 - 2/3 - 4/27 (By (a))
= 5/27

15 P(She pass the test)

= P(pass the test|revision)P(revision) + P(pass the test| no revision)P(no revision)

= 0.85 * 0.2 + 0.65 * 0.8

= 0.69

16(a) P(crash the parked train)

= P(trun right at A) * P(straight ahead at B) * P(straight ahead at C)

= 1/3 * 2/3 * 2/3

= 4/27

(b) Penter the depot)

= P(trun right at A) * P(straight ahead at B) * P(trun right at C) + P(trun right at A) * P(trun right at B)

= 1/3 * 2/3 * 1/3 + 1/3 * 1/3

= 5/27