The IIT Madras BS Statistics for Data Science II (Stats 2) Quiz 1 paper sat on 11 Jul 2021, in the May 2021 term, set POD21QZAQPA: 8 questions for 25 marks in 120 minutes. Every question is below with its answer. Take it as a timed mock test to be marked, or read it through first.
Suppose that the number of people who visit a yoga academy each day is a Poisson random variable with mean 20. Suppose further that each person who visits is, independently, girl with probability 0.5 or boy with probability 0.5. Find the joint probability that exactly 8 boys and 12 girls visit the yoga academy on any particular day.
Correct answer
A producer of a certain type of electronic component ships to suppliers in lots of twenty. Suppose that 60% of all such lots contain no defective components, 30% contain one defective component, and 10% contain two defective components. A lot is picked, two components from the lot are randomly selected and tested, and neither is defective. What is the probability that two defectives exist in the lot?
Correct answer
0.2
0.045
0.028
0.034
Correct answer
0.028
There are two roads from A to B and two roads from B to C. Each of the four roads is blocked by snow with probability p, independently of the others. Find the probability that there is an open road from A to B given that there is no open route from A to C.
Correct answer
The probability that a hunter will shoot the target is 0.4 in each attempt. Assume that successive attempts are independent. What is the probability that the hunter will shoot the target before the 5th attempt? Enter your answer correct to two decimals accuracy.
Correct answer: 0.87 (accepted within ±0.02)
A publisher claims that the probability of a page in a book being error-free is 0.9 You select a book of 500 pages. If you find the third misprint on the 6th page, what is the (conditional) probability that the fifth misprint will occur on the 10th page? Enter the answer correct to four decimal places.
Correct answer: 0.02435 (accepted within ±0.00035)
Correct answer: 0.007 (accepted within ±0.001)
Let an urn contain 3 Red colored balls, 3 Blue colored balls and 3 Green colored balls. The three different balls of each color are marked with numbers one, two and three, respectively. For each color, we toss a fair coin. If the coin lands head, we randomly choose a ball of that color from the urn. If the coin lands tail, no ball of that color will be removed. Repeat the above process for each of the three different colors. Find the probability that the sum of numbers obtained is more than 7. Enter the answer correct to four decimal places.
Correct answer: 0.0185 (accepted within ±0.0002)
