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i would like any help or suggestions you have please as i am very stcuk on these questions thanks

here is the scene:
each phone call made to the emergency services has probability 0.02 that it is not legitimate. assume that the legitimacy of one call is independant of weather or not other calls are legitimate.
here are the questions:
choose the option that is closet to:
A) the probability that the first call which isnt legitamate occurs on the 20th call
b) the probability that they receive at least 100 calls before they receive one which isnt legitamate
c)the probability that in a 150 calls, at least one is not legitamate

the chooses of answers are:
0.003 0.014 0.048 0.133 0.668 0.681 0.867 0.952

any ideas would be great hanks

A) 19 legitimate calls followed by a on legitimate one. Probability is:

0.98^19 * 0.02

B) 100 legitimate calls, after which it doesn't matter what happens. Probability is:



Probability that all 150 are legitimate is 0.98^150, so the probablity that one or more are not legitimate is:

1 - 0.98^150

the response i got here i don't understand. what does the ^ stand for?
i have tried the way that you have said but i don't get any answers which match the ones i can choose from please please help thak you very mcuh

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