CSE230Assignment 3 Solution

Lec1.ture 9:
2. According to estimates, 44 percent of Bangladeshis have blood type B+. Suppose,you have started to sample people as you are looking for B+ blood type. Once youprobability that you'll need to sampletype B+? What is the expected number of people to sample in order to ind someonewith that blood type and what is the standard deviation?ind a person with B+ blood type, you’ll stop sampling immediately. What's theexactly 6 people to ind someone with blood
3. Shomee is rolling a die repeatedly. What is the probability that a six will emergetsix and what is the standard deviation of the number of rolls?he irst time on the ifth roll? What is the expected number of rolls to get the irstfor
It's estimated that only about 5% of the population has hazel eyes. What is theprobability that onlyCalculate the mean and the variance of the number of hazel-eyed people from agathering of 150 people10 .people from a gathering of 100 people have hazel eyes?
Lec1.ture 10:
Suppose 4% of the toys in a batch will malfunction. Use the Poisson approximationto calculate the probability that in a big batch of 400 there will betoy. at most 1 defective
2. Ships dock at a bay at an average rate of 180 per hour.a. What is the probability that no ship docks in a minute?
b. Calculate the expected number of docking in 10 minutes
3. In a football match, suppose that the probability of Team A winning is 0.3, Team Bwinning is 0.5 and the rest is the probability of a Tie. If 30 games are played, what isthe probability that all games end in a Tie?
4. A baseball player is said to “hit for the cycle” if he has a single, a double, a triple, anda home run all in one game. Suppose these four types of hits have probabilities 1/16,1eight times and (b) four times?/4, 1/5, and 1/24. What is the probability of hitting for the cycle if he gets to bat (a)
Lecture 11 & 12:
1. An urn contains 6 red, 7 blue, and 5 green balls. You draw out two balls and they aredifferent colors. Given this, what is the probability that the two ballswere red and blue?
2. The following is a table showing the number of regular and irregular students inCSE230 live consultation hours and their grades in the viva voce .
Good Average Bad Total
Regular 22 2 x 5z-5
Irregular v u w z+3
Total 23 u+2 u-v 40
What is the probability that a student gets a bad grade in vivairregular in consultation? [Hint: You need to determine the unknowns irst]given that s/he is
3. An almost out-of-business movie theatre has three categories of seats - front,middle, and rear. Of the total number of seats, 10% are front seats, 30% are middleseats, and the rest are rear seats. It is known from previous experience ofmovie-goers that 5% of the front seats, 10% of middle seats, and 20% of the rearseats are broken. Determine the probability of a randomly selected seat beingbroken.
4. An insurance company classi ies people into one of the three classes – good risks,average risks and bad risks. 30% of the population are labelled as "good risk", 60%as "average risk" and the remaining as "bad risk".1-risk people are involved in an accident.Determine the probability of a randomlyselected policy holder being involved in an accident.year span 10% of good risk people, 20% of average risk people, and 30% of bad Their records indicate that over a
5. Bag A contains 6 red and 7 black balls and Bag B contains 9 red and 6 black balls.One ball is transferred from Bag A to Bag B and then a ball is drawn from Bag B. Theball so drawn is found to be black in color. Find the probability that the transferredball was red.
6. Suppose there are 8 fair coins and 12 unfair coins in a bag such that the unfair coinshave a 75% probability of landing heads. A coin is randomly picked from the bag andlipped 9 times. If the coin landed heads 7 times out of 9, what is the probability thatthe coin to be unfair?
7. Assume that the chances of the patient having a heart attack are 40%. It is alsoassumed that a meditation and yoga course reduces the risk of heart attack by 30%and prescription of certain drugs reduces its chances by 25%. At a time, a patientcan choose any one of the two options with equal probabilities. It is given that aftergoing through one of the two options the patient selected at random suffers a heartattack. Find the probability that the patient followed a course of meditation andyoga?