State true or false.If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is 0.5.

Engineering

Mathematics

Conditional Probability

Question

State true or false.

If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is 0.5.

True

False

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P(A) → 0.2

P(B) → 0.3

P(AUB) → probability that either A or B fails

P(AUB) → P(A) + P(B) – P(A∩B)

we know,

P(A∩B) → P(A) x P(B)

= 0.2 x 0.3

P(A∩B) = 0.06 – 1

so,

P(AUB) → 0.2 + 0.3 – 0.06

= 0.5 – 0.06

= 0.44

SO, P(AUB) → 0.44

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