You have studied the number of people waiting in line at your bank on Friday afternoon at 3 pm for many years, and have created a probability distribution for 0, 1, 2, 3, or 4 people in line. The probabilities are 0.1, 0.3, 0.4, 0.1, and 0.1, respectively. What is the probability that at most 3 people are in line at 3 pm on Friday afternoon?

Answer 1

There could be three persons in line at most.

#P(X=0) + P(X=1) + P(X=2) + P(X=3)# # = 0.1 + 0.3 + 0.4 + 0.1 = 0.9#
Thus # P(X<= 3) = 0.9#

Using the compliment rule would make this question simpler, though, as you can simply deduct the value you are not interested in from the total probability.

as:

#P(X<=3) = 1 - P(X>=4)# # = 1 - P(X=4) = 1 - 0.1 = 0.9#
Thus #P(X<= 3) = 0.9#
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Answer 2

To find the probability that at most 3 people are in line at 3 pm on Friday afternoon, we sum the probabilities of having 0, 1, 2, or 3 people in line:

P(at most 3 people) = P(0 people) + P(1 person) + P(2 people) + P(3 people) = 0.1 + 0.3 + 0.4 + 0.1 = 0.9

Therefore, the probability that at most 3 people are in line at 3 pm on Friday afternoon is 0.9.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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