Answer:
The probabilities are,
i) 0.015 or 1.5%
ii) 0.085 or 8.5%
iii) 0.135 or 13.5%
iv) 0.765 or 76.5%
Explanation:
The probability that 2 independent events happen is the product of the probabilities of the independent events,
probability that Arun is late for school is 0.1.
A = 0.1
The probability that Marcus is late for school is 0.15
M = 0.15
where A and M are the respective probabilities,
i) they are both late for school
we just multiply the probabilities of the independent events,
P = AM = (0.1)(0.15)
P = 0.015
ii) Arun is late but Marcus is not
The probability that Marcus is not late is, 1 - probability that he is late,
(1 since either he is late or he is not late)
NM = 1 - (0.15)
NM = 0.85
Multiplying this with A,
P = (A)(NM)
P = (0.1)(0.85)
P = 0.085
iii) Marcus is late but Arun is not
The probability that Arun is not late is 1 - probability that he is late,
NA = 1 - 0.1
NA = 0.9
Multiplying this with M,
P = (NA)(M)
P = (0.9)(0.15)
P = 0.135
iv) neither of them is late for school.
This is the product NA and NM,
P = (NA)(NM)
P = (0.9)(0.85)
P = 0.765