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The probability that the company will have to pay at least $150,000 in benefits next year is 0.047 if the there are 120 women.
What is probability?
It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.
The probability of dying:
P(dying) = 1/150
P(living) = 1 - P(dying) = 1 - 1/150 = 140/150
There are 120 women.
P(x≥3) = 1 - [P(x=0) +P(x=1) + P(x=2)]
[tex]\rm P(x\geq 3)=1-[(120 \ choose \ 0)(1/150)^0)((149/150)^{120})+[/tex]
[tex]\rm (120 \ choose \ 1) ((1/150)^1) ((149/150)^{119}) +[/tex]
[tex]\rm (120 \ choose \ 2)((1/150)^2)((149/150)^{118})][/tex]
P(x≥3) = 0.047
Thus, the probability that the company will have to pay at least $150,000 in benefits next year is 0.047 if the there are 120 women.
Learn more about the probability here:
brainly.com/question/11234923
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