Search & Filtering
If A and B are events such that P(A) = 0.6, P(B|A) = 0.3 and P(A ∪ B) = 0.72. Are A and B independent, mutually exclusive or both?
. An X-ray test is used to detect a disease that occurs, initially without any symptoms, in 3% of the population. The test has the following error rates: • 7% of people who are disease free have a positive reaction; • 2% of the people who have the disease have a negative reaction. A large number of people are screened at random using the test, and those with positive reaction are taken for further examination. (a) What proportion of people who have disease are correctly diagnosed? (b) What proportion of people with a positive reaction actually have the disease? (c) What proportion of people with negative reaction actually have the disease? (d) What proportion of the test conducted give incorrect diagnosis?
Two machines are producing the same item. The previous week, Machine A produced 40% of the total output, and Machine B the remainder. On average, 10% of the items produced by Machine A were defective, and 4% of the items produced by Machine B were defective. (a) What proportion of the previous week’s entire production was defective? (b) If an item selected at random from the combined output is found to be defective, what is the probability it came from Machine A?
The probability that a student passes Probability is 0.8 if she studies for the exam and 0.3 if she does not study. If 60% of the class studied for the exam, and a student picked a random from the class has passed, what is the probability that she studied for the exam?
Suppose there are n people in a room. (a) What is the probability that at least two are born in the same month? Assume all the months are equal. (b) What is the probability if n = 13?
The friends send emails about the opening night to 128 people
They ask each person contacted to forward an email to five people on exchange for entry into a prize draw for a free meal for 2
Based on the assumptions below, how many people who received an email would you expect to attend the opening night.
Assumptions:
Half of the 128 people forward the email to 5 others
1/4 of these forward the email to 5 others
1/8 these forward the email to 5 others
1/16 these forward the email to 5 others
No one receives the email more than once.
10% of the people who receive an email go to the opening night.
There are 12 eggs in a pack. 4 are spoiled ones. If 2 of them are randomly selected, calculate the probability that at least one of them is faulty
1. The checking accounts of Sun Bank are categorized by the age of account and the account balance. Auditor will select accounts at random from the following 1000 accounts
a) What is the probability that an account is less than 2 years old?
b) What is the probability that an account has balance of $1000 or more?
c) What is the probability that the two accounts will both have a balance of $1000 or more?
d) What is the probability that an account has a balance of $500-$999 given that its age is 2 years or more?
e) What is the probability that an account is less than 2 years old and has a balance of $1000 or more?
f) What is the probability that an account is at least 2 years old given that the balance is $500-$999?
The average daily jail population in the New Bilibid prison in Muntinlupa City is 36,295. If the distribution is normal and the standard deviation is 3,760, find the probability that on a randomly selected day, the jail population is greater than 40,145.
1. Consider the set of even single-digit number {0, 2, 4, 6, 8}. a. Make a list of possible sample size of 2 that can be taken from this sets of numbers
