Find the probability that both sellers are free

Problem description:
There are two sellers working in a small store.
At a random point in time, each of them can be engaged in customer service with a probability of 0.3.
Moreover, they can be occupied simultaneously with a probability of 0.1.
Find the probability that at a random moment in time
a) both sellers are free;
b) one of them is free, and the other is busy.

Problem solution:
(a)

Find the probability that at a random moment both sellers are free

Let define event A as seller #1 is busy and event B as seller #2 is busy.
Then P(A∪B) - the probability that at least one of the sellers is busy.

According to the probability addition formula is:
P(A∪B) = P(A) + P(B) - P(A∩B) = 0.3 + 0.3 - 0.1 = 0.5

Then the probability that both sellers are free is:
1 - P(A∪B) = 1 - 0.5 = 0.5.

Answer: probability that both sellers are free is 0.5


(b)

Find the probability that one seller is busy, and the other is free

In this situation, there are four possible options with sellers:
1) seller #1 is free and seller #2 is busy;
2) seller #2 is free and seller #1 is busy;
3) both sellers are free (probability of this event = 0.5);
4) both sellers are busy (probability of this event = 0.1).
Therefore, the probability of the first and second option is equal to: 1 - 0.5 - 0.1 = 0.4

Answer: probability that one seller is free, and the other is busy equals 0.4

Next probability problem solution: Find the probability that two purchased batteries will be working.

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Monday, November 23, 2020
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