1 foot = 
yard
1431 ÷ 3 = 477 yards
1431 ÷ 3 = 477 yards
Which statement is true about whether Z and B are independent events?
1 answer:
Answer:
Z and B are independent events because P(Z∣B) = P(Z).
Step-by-step explanation:
After a small online search, I've found a table to complete this problem, that we can see below.
For two events Z and B, we have:
P(Z|B) = probability of Z given that B
such that:
P(Z|B) = P(Z∩B)/P(B)
So, two events are independent if the outcome of one does not affect the outcome of the other.
So, if the probability of Z given B is different than P(Z) (the probability of event Z) means that the events are not independent.
So Z and B are independent if the probability of Z given B is equal to the probability of Z.
P(Z|B) = P(Z)
In the table we can see:
P(Z|B) will be equal to the quotient between all the cases of Z given B (126) and the total cases are given B (280)
P(Z|B) = 126/280 = 0.45
Similarly, we can find P(Z):
And P(Z) = 297/660 = 0.45
So we can see that:
P(Z|B) = P(Z)
Thus, B and Z are independent.
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Answer:
a) 0.98% probability that 17 of the 29 people are men.
b) 3.86% probability that the first woman is reached on the 8th call
Step-by-step explanation:
For each person chosen by the agency, there are only two possible outcomes. Either it is a man, or it is a woman. The probability of selecting a man or a women in each trial is independent from other trials. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
(a) What is the probability that 17 of the 29 people are men?
This is P(X = 17) when . So
0.98% probability that 17 of the 29 people are men.
(b) What is the probability that the first woman is reached on the 8th call?
On the first 7 trials, all men, each with a 78% probability.
On the 8th trial, a women, with a 22% probability. So
3.86% probability that the first woman is reached on the 8th call