Question

1. Of Starfleet personnel, 40% are non-human, and 20% are left-handed. 56% are right-handed humans. We randomly select a member of Starfleet. Given the characteristics “human”, and “right-handed”, find the various probabilities following a random selection:

a) the probability the selection possesses exactly one of these characteristics

b) the probability the selection neither of these characteristics

c) the probability the selection possesses at least one of these characteristics

Answer 1

Let H indicate the event, "human" and R indicate the event "right-handed"

P(H') = 0.4

P(H) = 1 - 0.4 = 0.6

P(R') = 0.2

P(R) = 1 - 0.2 = 0.8

P(H R) = 0.56

a) P(exactly one the characteristics) = P(H) + P(R) - 2P(HR)

= 0.6 + 0.8 - 2x0.56

= 0.28

b) P(neither of these characterisctics) = 1 - P(H U R)

= 1 - [P(H) + P(R) - P(H R)

= 1 - (0.6 + 0.8 - 0.56)

= 0.16

c) P(at least one of these characteristics) = 1 - P(neither of these characteristics)

= 1 - 0.16

= 0.84