Is this a conditional probability or not?

Question

Suppose that the telephone calls during one minute time follow a Poisson distribution with mean=4. If people can handle at most 6 calls per minute, what is the probability that the people will receive more calls than they can handle during one-minute interval?

Hi,

I am just confused whether this question is conditional probability.

Since people can handle at most 6 calls during one-minute.

Probability of receiving more calls than they can manage is P(X>6), or is it a conditional probability? Given that they can handle at most 6 calls, Probability of receiving more calls than they can manage is P(X>6 given that X<=6) ?

Answer 1

This is just an unconditional probability. As you yourself suggest, you need to calculate $P(X>6)$, which is the probability of getting more than the number of manageable calls in a minute.

Answer 2

Looking at this as a conditional probability has no use. You can see that by your last statement:

P(X>6 given that X<=6) is always identically zero; if $X\leq 6$ then $X$ is never greater than 6.

Conditional probabilitiees are a meaningful concept when a problem involves two or more random variates (generally non-independent variates).

Answer 3

I think this question is about unconditional probability. A conditional version of the problem would have been : "give the probability that the people can't handle all the calls given the fact the phone has already rung 3 times".