please help cuz i been trying for ages and cant get the answer
each telephone call made to the emergency services either is or is not legitimate. suppose that each call received has probability 0.02 that it is not legitimate. assume that the legitimacy of one call is independent of whether or not other calls are legitimate.
(the choices of answers are at the bottom of the page)
QU1) whats the closet option that they receive at least 100calls before they receive one which is not legitimate?
qu2) whats the closet option that in 150calls at least one is not legitimate?
the choices of answers are:
0.003
0.014
0.048
0.133
0.668
0.681
0.867
0.952
Q1) probability of exactly 100 consecutive "good" calls = (0.98)^100 = 0.133
That satisfies the "at least 100" criterion.
Q2)The probability that all of 150 calls are legitimate is (0.98)^150 = 0.048. One minues that, or 0.952, is the probability that at least one is NOT legitimate.
To solve these questions, we need to use the concept of probability.
Q1) The probability of each call being legitimate is 0.98 since the probability of a call not being legitimate is given as 0.02. The question asks for the closest option where at least 100 calls are received before receiving one that is not legitimate.
The probability of exactly 100 consecutive legitimate calls is calculated by raising 0.98 to the power of 100 (0.98^100), which equals 0.133. This satisfies the condition of "at least 100" calls.
Therefore, the closest option to the answer is 0.133.
Q2) The probability of all 150 calls being legitimate is calculated by raising 0.98 to the power of 150 (0.98^150), which equals 0.048.
The question asks for the closest option where at least one call is not legitimate. To find this probability, we subtract the probability of all calls being legitimate from 1. Therefore, the probability of at least one call not being legitimate is 1 - 0.048, which equals 0.952.
Therefore, the closest option to the answer is 0.952.