Easy Probability Q

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The probability that shares in the Bank of Lapland will rise on any given day is 0.4, while the probability that shares in the Bank of Never Never Land will rise on any given day is 0.73. Assume that these two events are independent. Give all answers correct to two decimal places.

I just want to know how to work out the answers when i have the answers already! :mad::eek:

Q1 What is the probabilty that both of these events occur?
Expected answer:
0.29

Q2 What is the probabilty that neither of these events occur?
Expected answer:
0.16

Q3 What is the probabilty that at least one of these two events will occur?
Expected answer:
0.84

Q4 What is the probabilty that only one of the two events occur?
Expected answer:
0.55

spock.

First it's best to name the events, A and B

Q1. The probability that 2 independent events A and B occur is P(A) * P(B)
= 0.73 * 0.4 = 0.29

Q2. The probability that an event A does not occur is 1-P(A).
So the probability A doesn't occur 1- 0.73 = 0.27 and probability B doesn't occur is 1- 0.4 = 0.6
The events are independent so both don't occur 0.6 * 0.27 = 0.16

Q3. We have the probability that neither occur (Q2, 0.16) and either neither occur or at least one occurs therefore P(at least one) is given by 1-P(0) = 1-0.16 = 0.84

Q4 Only one occurs if A does and B doesn't or vice versa.
Probability of A occurring and B not occurring is P(A) * (1-P(B) = 0.73 * 0.6 = 0.44
Probability of B occurring and A not occurring is P(B) * (1-P(A) = 0.27 * 0.4 = 0.11
The probability of exactly one occurring is found by adding these together, 0.44 + 0.11 = 0.55

Yakuza

For part (iv) you can also say
P(one occurring) = 1 - (p(both occur) + p(neither occur)) or 1 - (0.29 + 0.16) = 0.55.
I think this is easier than working out A and (not plus B and (not A), but you get the same answer in the end.

spock.

Oh good point, not sure how I didn't spot that.

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Thanks spock and yakuza for the posts, appreciate it a lot!!