In April 2025
Search & Filtering
Let A and B be two events associated with an experiment and suppose that P(A)=0.4 while P(AUB)=0.7. Let
P(B)=P
a) For what choice of P are A and B mutually exclusive?
b) For what choice of P are A and B independent?
In a large graduating class of 100 students 54 studied mathematics, 69 studied library science, and 35 studied
both mathematics and library science. If one of these students is selected at random, find the probability that
a) The student takes mathematics or library science
b) The student does not take either of these subjects
c) The student takes library science but not mathematics
In how many ways can a committee of three be chosen from 4 married couples if
a) All are equally eligible?
b) One particular man must be on the committee?
A population consists of the numbers 1, 2, 3, and 4 with the sample size of 2 (without replacement). Which mean that has a probability of 2/6 or 1/3 or 0.33?
If the events have the same theoretical probability of happening, then they are called
Consider a population consisting of the values (1, 3, 8), n= 2 with replacement.
- Identify the probability of each sample
The time taken to assemble a car in a certain plant is a random variable having a normal
distribution of 20 hours and a standard deviation of 2 hours. What is the probability that a
car can be assembled at this plant in a period of time less than 19.5 hours?
1. If a population has a mean of 5.7, what is the mean of the sampling distribution of its means?
1. Before students wrote a mathematics examination, their teacher had made predictions about the results that students will receive. After the actual results of the examinations, the results for 150 candidates were classified according to whether the predicted grade was better than, equal to, or worst than the actual grade, as shown in the following table:
Predicted grade
Actual
Grade Obtained
Better
Equal
Worst
B
16
30
12
58
C
10
20
9
39
D
20
15
18
53
46
65
39
150
Carry out a χ2 test at the 5% level of significance to determine whether the teachers prediction and the actual results are independent.
1. In a survey of 1500 households, it is found that 47% of them have a high-definition television (based on data from the consumer electronics association). Use a 0.01 significance level to test the claim that fewer than half of all households have a high definition television. Are the results from a few years ago likely to be valid today?
