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:
0.98^100
C)
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
I apologize for the confusion. The "^" symbol stands for exponentiation, meaning raising a number to a power. For example, if I have 2^3, it means 2 raised to the power of 3, which is equal to 2 * 2 * 2, resulting in 8.
Let's go through the calculations step by step for each question:
A) The probability that the first call which isn't legitimate occurs on the 20th call:
We need to calculate the probability that the first 19 calls are legitimate (0.98^19), and then multiply it by the probability that the 20th call is not legitimate (0.02).
So the calculation is: 0.98^19 * 0.02
B) The probability that they receive at least 100 calls before they receive one which isn't legitimate:
We want to find the probability that the first 100 calls are all legitimate, which is 0.98^100. Since it doesn't matter what happens after that, we can just calculate the probability of the first 100 calls being legitimate.
So the calculation is: 0.98^100
C) The probability that, in 150 calls, at least one is not legitimate:
We can find the probability that all 150 calls are legitimate (0.98^150), and then subtract it from 1 to get the probability that at least one call is not legitimate.
So the calculation is: 1 - 0.98^150
After performing these calculations, you can compare the results with the answer choices provided to see which one matches the closest. If the calculations are not matching any answer choices, please double-check your calculations or let me know the specific results you obtained, and I'll be glad to assist you further.