Question

difference between atleast and atmost in probability with example?

Answer 1

At most means maximum, whereas at least means minimum.

Let me explain with the help of an example.

Suppose that X takes values 0, 1, 2, 3 . . . . . . 6 with certain probabilities and we have to calculate the probability that:

X is at least 4

X is at most 4

Then:

In the first point, the phrase ‘X is at least 4’ means that the least X is allowed to be is 4; it can be 4, or any number greater than 4.

Thus, P(X is at least 4) = P(X≥4) = P(X=4)+P(X=5)+P(X=6)

Similarly, In the second point, the phrase ‘X is at most 4’ means that the most X is allowed to be is 4; it can be 4, or any number less than 4.

Thus, P(X is at most 4) = P(X≤4) = P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)