Answers:
- probability = 0.18
- probability = 0.70
- About 2.03 accidents per day on average
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Explanation:
Problem 1
Add up the given probabilities in the bottom row:
0.12+0.32+0.25+0.13 = 0.82
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.
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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.
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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".
