Stepwise
Start practisingPractise

WAEC 2009 · Paper 2 · Q3

The probability that a malaria patient MM survives when given a newly discovered drug is 0.270.27, and the probability that a typhoid patient TT survives when injected with another newly discovered drug is 0.850.85. Give your answers correct to 2 significant figures.

  1. (a)

    What is the probability that either of the two patients survives?

  2. (b)

    What is the probability that neither of the two patients survives?

  3. (c)

    What is the probability that at least one of the two patients survives?

Worked solution (try it first)
  1. Write down the probabilities of not surviving: P(M′)=1−0.27=0.73P(M') = 1 - 0.27 = 0.73 and P(T′)=1−0.85=0.15P(T') = 1 - 0.85 = 0.15.

(a)

  1. "Either survives" means exactly one of them survives: MM survives and TT does not, or TT survives and MM does not.
  2. P=0.27×0.15+0.85×0.73P = 0.27 \times 0.15 + 0.85 \times 0.73
    =0.0405+0.6205= 0.0405 + 0.6205
    =0.661= 0.661, which is 0.660.66 to 2 s.f.

(b)

  1. Neither survives: 0.73×0.15=0.10950.73 \times 0.15 = 0.1095, which is 0.110.11 to 2 s.f.

(c)

  1. At least one survives is everything except "neither": 1−0.1095=0.89051 - 0.1095 = 0.8905, which is 0.890.89 to 2 s.f.

Report a problem with this question