There is a .97 chance that no accident will occur during any particular day at a racetrack of local importance. the probability of one accident a day is .02, and the probability of two accidents is .01.
a. What is the expected number of accidents in a day?
b. What is the expected number of accidents in ten days?
I just don't understand how to set these questions up and any help would be much appreciated.
PLease help. I need this asap and I don't even know how to work it
To solve these questions, we will use the concept of expected value, which is a measure of the average outcome of a random event.
a. What is the expected number of accidents in a day?
To calculate the expected number of accidents in a day, we need to multiply the number of accidents by their probabilities and sum them up.
Let's denote the number of accidents as A.
The probability of no accidents occurring (A = 0) is given as 0.97.
The probability of one accident occurring (A = 1) is given as 0.02.
The probability of two accidents occurring (A = 2) is given as 0.01.
We can calculate the expected number of accidents as:
Expected number of accidents = (number of accidents * probability) + (number of accidents * probability) + ...
Expected number of accidents = (0 * 0.97) + (1 * 0.02) + (2 * 0.01)
Calculating the above expression:
Expected number of accidents = 0 + 0.02 + 0.02
Hence, the expected number of accidents in a day is 0.04.
b. What is the expected number of accidents in ten days?
To calculate the expected number of accidents in ten days, we can use the linearity property of expected value. This property tells us that the expected value of the sum of several random variables is equal to the sum of their individual expected values.
So, we can find the expected number of accidents in ten days by multiplying the expected number of accidents in one day by ten.
Expected number of accidents in ten days = 10 * (Expected number of accidents in one day)
Substituting the value we found in question a:
Expected number of accidents in ten days = 10 * 0.04
Hence, the expected number of accidents in ten days is 0.4.