## Spike is not a terribly bright student. His chances of passing chemistry are 0.35; mathematics, 0.40; and both, 0.12. Are the events “Spike

Question

Spike is not a terribly bright student. His chances of passing chemistry are 0.35; mathematics, 0.40; and both, 0.12. Are the events “Spike passes chemistry” and “Spike passes mathematics” independent? What is the probability that he fails both subjects?

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3 weeks 2021-09-28T17:46:45+00:00 1 Answer 0

The events “Spike passes chemistry” and “Spike passes mathematics” are not independent.

The probability that he fails both subjects = 0.37

Step-by-step explanation:

The probability of Spike passing Chemistry = P(Chemistry) = 0.35

The probability of Spike passing Mathematics = P(Mathematics) = 0.40

The probability of Spike passing both Chemistry and Mathematics = P(Chemistry,Mathematics) = 0.12

For the events “Spike passes chemistry” and “Spike passes mathematics” to be independent, P(Chemistry,Mathematics) should be equal to P(Chemistry) * P(Mathematics)

But P(Chemistry) * P(Mathematics)=0.35*0.40 =0.14

So the two events are not independent.

The Probability that he passes Chemistry or Mathematics is given by P(Chemistry) + P(Mathematics) – P(Chemistry,Mathematics)

= 0.35+0.40-0.12=0.63

So the probability that he fails both subjects is the complement of this, namely (1 – 0.63) = 0.37