HELP PLS! Suppose the year of car accidents per day in Wilmington NC has been recorded for the past year. The table below is a probability distribution table representing the data collected.
1) what is the probability that on a randomly selected day there were no accidents?

2) find the probability there will be at least 2 accidents

3) on any given day how many accidents should the Wilmington police expect to have.

For any probability distribution, all of the probabilities must add to 1. This represents 100%. If x is the probability of getting 0 accidents, then x+0.82 = 1 solves to x = 0.18

Having 0.18 in that blank spot will add to the other probabilities to get a total sum of 1.

--------------------------

Problem 2

Add up every probability that corresponds to "2 accidents" or more.

0.32+0.25+0.13 = 0.70

There's a 70% chance of having 2 or more accidents.

--------------------------

Problem 3

Add in a third row that multiplies the first two rows. If x = number of accidents, and P(x) = probability, then we'll have an x*P(x) row. Check out the table in the attached image.

After determining that third row, add up those products.

0 + 0.12 + 0.64 + 0.75 + 0.52 = 2.03

For any given day, we expect there should about 2.03 accidents on average.

This lines up with the table showing that P(x) is largest when x = 2; ie 0.32 is the largest probability in the table corresponding to having 2 accidents.

For more information, check out "expected value".