Answer:
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
