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The probability that Arun is late for school is 0.1. The probability that Marcus is late for school is 0.15. These are independent events. Work out the probability that

i) they are both late for school
ii) Arun is late but Marcus is not
iii) Marcus is late but Arun is not
iv) neither of them is late for school. ​

1 Answer

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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

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