急! F5 Probability 05q5

23.
(a)
P(both B and C malfunction)
= P(B malfunction) x P(C malfunction)
= 0.3 x 0.4
= 0.12

(b)
P(the device NOT functions properly)
= P([A malfunction] or [B and C malfunction])
= P(A malfunction) + P(B and C malfunction) - P(A, B and C malfunction)
= 0.2 + 0.12 - 0.2 x 0.3 x 0.4
= 0.296

P(the device functions properly)
= 1 - P(the device NOT functions properly)
= 1 - 0.296
= 0.704


24.
(b)
P(overpass) = 4/7
P(tunnel) = 2/7
P(hill road) = 1 - [(4/7) + (2/7)] = 1/7

(I)
P(overpass and overpass)
= P(overpass) x P(overpass)
= (4/7) x (4/7)
= 16/49

(II)
P(at least one journey passes through hill road or tunnel)
= 1 - P(overpass and overpass)
= 1 - (16/49)
= 33/49

(III)
P(both journeys neither overpass nor tunnel)
= P([hill road] and [hill road])
= P(hill road) x P(hill road)
= (1/7) x (1/7)
= 1/49