Consider three boxes containing a brand of light bulbs. Box I contains 6 bulbs of which 2 are defective, Box 2 has 1 defective and 3 functional bulbs and Box 3 contains 3 defective and 4 functional bulbs. A box is selected at random and a bulb drawn from it at random is found to be defective. Find the probability that the box selected was Box 2!

Q: There are 6 boxes, 2 of type A and 4 of type B. Type A boxes each contain 2 green marbles and 3 red…

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Q: Suppose an urn contains 12 balls, with 7 red and 5 black. If you randomly select 4 balls without…

A: Introduction: According to the permutation rule, if r distinct items are to be chosen from n items…

Q: Suppose you have three bowls, XX, YY, and ZZ, each with four balls with XX having 3 red and 1 blue,…

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Q: In a country, 80% of the graduates are citizens,65% of the citizens graduates are employed while…

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Q: A random sample of adults that arrive late to work found that 50% of the time was because of rain,…

A: It is given that, The probability that adults arrive late due to rain is = P(rain) = 0.50 The…

Q: A bag 'A' contains 2 white and 3 red balls and a bag 'B' contains 4 white and 5 red balls. One ball…

A: We have to find given probability.

Q: Suppose that 10% of a certain batch of calculators have a defective case, and that 12% have…

A: Here we will use addition theorem of probability  P(A∪B)=P(A)+P(B)-P(A∩B) A∪B  denotes A or B ( At…

Q: in the happy hilltop health home, 10% of the sesidents play shuffleboard, 35% of the residents play…

A: Let A be the event such that the residents play shuffleboard, B be the event such that residents…

Q: In a certain residential suburb, 60% of all households get Internet service from thelocal cable…

A: Given data: The given percentage of the users who get internet service is P(A)=60%=0.60. The given…

Q: Suppose that a box containing music CDs has 4 with country music, 6 with rock music, 3 with jazz…

A: A box containing music CDs has 4 with country music, 6 with rock music, 3 with jazz music, and 7…

Q: Consider three boxes containing a brand of light bulbs. Box I contains 6 bulbs of which 2 are…

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Q: Teledex Corporation is going to hire 3 programmers from a pool of 5 female and 5 male applicants.…

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Q: Suppose that 80% of all customers who regularly purchased in this store choose an electronic…

A: Let  K be the event for Keyboard G be the event for guitar C be the event for cello

Q: A financial services committee had 6060 ​members, of which 88 were women. If 77 members are selected…

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Q: Given two urns: U contains 4 red and 6 green balls and V contains 5 red and 6 green balls. A ball is…

A: Define some events A : a red is selected from U B : a green ball ia selected from U. E : two balls…

Q: In a certain residential suburb, 60% of all households get internet service from the local cable…

A: Here the given information,Let A: households get- internet service from the local cable company.…

Q: A financial services committee had 60 ​members, of which 10 were women. If 8 members are selected…

A: Basic concepts of Probability and Permutation-Combination are used.

Q: A subcommittee is to be selected from a committee of men and women. For this problem, assume that…

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Q: what is the probability that the other side is colored black?

A: Our aim is to find the probability that the other side is colored black.

Q: A sub-committee of 6 members is to be formed out of a group of 7 men and 4 ladies. Calculate the…

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Q: Suppose a Box contains 200 identical machine parts. Out of which 100 are produced by machine A, 60…

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Q: Assume that the box contains 10 balls: 2 red, 2 green, and 6 blue. 2 balls are drawn at random, one…

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Q: Box A contains 5 black marbles and 4 white marbles, and Box B contains 3 black marbles and 2 white…

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Q: In a company of 400 employees,250 use a computer and 100 use a telephone as part of their work. The…

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Q: In a class of 25 students, 3/5​ of the class are boys, 2/5of the class have ​blonde hair, and 1/5​…

A: We have to find given probability.

Q: Suppose that each of three men at a party throws his hat into the center of the room. The hats are…

A: Probability of an event is equal to the ratio of number of favourable outcomes to total number of…

Q: A box contains 20​ chocolates, but only two of them are the dark chocolate that somebody likes. When…

A: Theoretical Probability:Probability of an event is the number of outcomes favourable to the event,…

Q: Suppose Julia owns a pen manufacturing company and determines that 3 out of every 75 pens are…

A: Here given that 3 out of every 75 pens are defective.  So , p = 3 / 75

Q: A particular slot machine in a casino has payouts set so that the probability of winning money in…

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Q: In a country, 75% of the graduates are citizens,60% of the citizens graduates are employed while…

A: Given , 75 percent of the graduates are citizens ... Among them 60 percent of citizens are employed…

Q: Box A contains 8 items of which 3 are defective, and box B contains 5 items of which 2 are…

A: Solution To find the probability we will use conditional probability formula and total probability…

Q: Suppose that the population of a certain city is 40% males and 60% females. Suppose also that 50% of…

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Q: A flashlight has 8 batteries, 4 of which are defective. If 4 are selected at random without…

A: Solution: Given information: Total batteries = 4 defective + 4 non defective =8 Total batteries=8…

Q: Consider three boxes containing a brand of light bulbs. Box I contains 6 bulbs of which 2 are…

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Q: The physics department of a college has 10 male professors, 6 female professors, 13 male teaching…

A: Given that, Number of male professors = 10 Number of female professors = 6 Number of male teaching…

Q: A team of 5 men and 4 women is to be chosen at random from a group of 8 male and 7 female…

A: The formula for combination is nCr = n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)]/r!. Explanation:…

Q: In a survey, 422 people indicated they prefer pepperoni pizza, 80 indicated they prefer cheese…

A: Solution: From the given information, total number of people is 422. Out of which 80 indicated they…

Q: Assume that the committee consists of 8 Republicans and 7 Democrats. A subcommittee of 6 is randomly…

A: Obtain the probability that the new subcommittee will contain at least 2 Democrats. The probability…

Q: Suppose that 20% of the adult population in Palestine smoke cigarettes only, 15% smoke Argeeleh…

A: C be the event of smoking cigarettes only. P(C)=0.20 A be the event of smoking Argeeleh only.…

Q: In a country, 80% of the graduates are citizens,65% of the citizens graduates are employed while…

A: Solution: Probability P(E)=( Number of favourable outcomes n(E)) ÷ ( Number of total possible…

Q: Consider a collection of envelopes consisting of one red envelope, three blue envelopes, two green…

A: We have given that a collection of envelopes consisting of one red envelope, three blue envelopes,…

Q: There are 6 passengers on the bus, and there are 6 remaining stops before the end of the route.…

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Q: Consider 3 urns. Ballot box A contains 3 white balls and 8 red balls, ballot box B contains 9 white…

A: It is given that there are 3 ballot boxes, A, B, and C. The number of balls in each ballot box is:…

Q: A doorman is holding 9 keys in which only 1 key will work on room no. 3A. What is the probability of…

A: Given that  The doorman is holding 9 keys in which 1 key will work on room no. 3A Total keys = 9…

Q: (b) Among the 300 employees of a company, 240 are union members, whereas the others are not. If six…

A: Given Total number of employees in the company N = 300 Number of union members among the 300…

Q: At a certain restaurant, there is a 60% probability that the candles on your table will be red. If…

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Q: Consider three boxes containing a brand of light bulbs. Box I contains 6 bulbs of which 2 are…

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Q: A subcommittee is to be selected from a committee of men and women. For this problem, assume that…

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Q: Of the cartons produced by a​ company, 9​% have a​ puncture, 7​% have a smashed​ corner, and 0.5​%…

A: The general formula of probability is given by, P(A or B)=P(A)+P(B)-P(A and B) Given: 9​% have a​…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.