Suppose a box contains 4 defective batteries and 10 good batteries. If 2 batteries are drawn from the box without replacement, what is the probability that the following will occur? (Enter your probabilities as fractions.) (a) the first one is good and the second one is defective (b) the first one is defective and the second one is good (c) one of the batteries drawn is good and one of them is defective

Q: A company has 2 machines that produce widgets. An older machine produces 23% defective widgets,…

A: It is given that there are 2 machines in the company, one is older and other one is new.

Q: You have two boxes in front of you. You cannot see the contents of the boxes, but you are told that…

A: Box A: 2 red pencils Box B: 1 red pencil and 1 blue pencil. Let P(choosing Box A) = P(B1) = 12…

Q: box A contains 5 nickels and 3 quarters, while box b contains 8 nickels and 4 quarters. A coin is…

A: Consider, A and B be the event that show that coin is chosen from box A and box B respectively. N is…

Q: Suppose a box contains 13 marbles, 4 are red, 4 are blue, and 5 are yellow. Find the requested…

A: To find the Probability: (a) If two marbles are selected with replacement, the probability that one…

Q: Three boxes contain red and green balls. Box 1 has 5 red balls and 5 green balls, Box 2 has 7 red…

A: It is given that there are three boxes contain red and green balls. Box 1 contains 5 red balls and 5…

Q: You are playing a game where you must roll a fair die and then draw 2 balls, without replacing them,…

A: P( A : 1 or a 2) =13P( B : 3,4,5 or 6) =23 As to draw 2 green balls from the same bag,   P(G1 :2…

Q: 4. There are 6 black pens and 8 blue pens in a jar. If you take a pen without looking and then take…

A: Given: There are 6 black pens and 8 blue pens

Q: Two balls are drawn, without replacement, from a bag containing 11 red balls numbered 1-11 and 4…

A:

Q: Two balls are drawn, without replacement, from a bag containing 15 red balls numbered 1−15 and 8…

A: Given that:   A bag containing 15 red balls numbered 1−15 and 8 white balls numbered 16−23.   Total…

Q: To the right are the outcomes that are possible when a couple has three children. Assume that boys…

A: Given;Total events = 8Number of events that contains exactly three girls = 1The formula to calculate…

Q: A red ball and 8 white balls are in a box. If two balls are drawn, without replacement, what is the…

A: See the detailed solution below.

Q: very cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store…

A: Given : Total Boxes = 63 Out of them 19 of the boxes have the secret decoder ring And remaining…

Q: The damage in a structure after an earthquake can be classified as either none, light, or heavy. For…

A: The probabilities that it will suffer light and heavy damages after an earthquake are 2.5% and 1%,…

Q: Q2: Box 1 contains 30 red and 70 white balls, box 2 contains 50 red and 50 white balls, and box 3…

A: The probability that an even Ai (i=1(1)n) will occur given that a event B has already occurred is…

Q: Suppose that Karlyn’s store now contains 10 Hewlett-Packard computers, 5 Dell computers, and 5 Sony…

A: Given: A computer store contains, 10 Hewlett-Packard computers, 5 Dell computers, 5 Sony computers.…

Q: 4. Seth has 4 plaid shirts and 5 solid-colored shirts hang- ing together in a closet. In his haste…

A:

Q: There are two bags containing several colored balls. The bag B1 contains 17 red balls, 17 blue…

A: We have to use simple probability question.

Q: Suppose, Tonmoy, Sneha and Rashed are three friends who applied for a job in a company where the…

A: Given probability distribution is   P(T) =2/3 P(S) =1/3 P(R) =4/7

Q: Suppose you have three jars with the following contents: 2 black balls and 2 white balls in the…

A: Here we use bayes' theorem,

Q: A red ball and 7 white balls are in a box. If two balls are drawn, without replacement, what is the…

A: probability = favorable chance/total chance

Q: A car rental firm has 455 cars. Sixty-four of these cars have defective turn signals and 36 have…

A: Probability quantifies the chances of happening an event. The probability values always lie in the…

Q: Player 1 tosses N + 1 times a fair coin and player 2 tosses N times a fair coin. Player 1 wins the…

A: It is given that , player 1 tosses the coin N+1 times and player 2 tosses the coin at N times. Part1…

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: Suppose that in an assortment of 20 calculators there are 4 with defective switches. Draw with and…

A: Given, Total no of calculators (n) = 20 No of defective calculators (x) = 4 Draw with and without…

Q: 4. Matt, unhappy with his chance of success in the previous game, tries a new game. In this game,…

A:

Q: A dry cleaning firm has 20 employees: 13 women and 7 men. Two of the women and seven of the men are…

A:

Q: Suppose that on each play of the game a gambler either wins $1 with probability p = or loses $1 with…

A: According to the given problem, Gain=$1Probability of gain, p=23Loss=$1Probability of loss, q=13 a)…

Q: Suppose you have 3 nickels and 4 dimes in your right pocket and 2 nickels and a quarter in your left…

A: Consider the following, E=right pocket  is chosenF=left pocket is chosenN=selected coin is nickel…

Q: You have just bought a ticket for the chamber of commerce lottery, and your friend has brought two…

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

Q: Every morning a math instructor picks out two socks completely at random from his closet; there's…

A:

Q: A committee of three is to be formed from a group of 12 members; in which there are 6 females and 6…

A: Given: A committee of three is to be formed from a group of 12 members; in which there are 6 females…

Q: A red ball and 8 white balls are in a box. If two balls are drawn, without replacement, what is the…

A:

Q: A bag contains 8 white balls, 4 red balls, and 6 black balls. If 3 balls are drawn at random from…

A: From the provided information, Total white balls in bag = 8 Red balls = 4 Black balls = 6 Let W…

Q: Three boxes contain red and green balls. Box 1 has 5 red balls and 5 green balls, Box 2 has 7 red…

A: Let A, B, C are the probabilities of choosing a box. PA=14, PB=12,PC=14

Q: Suppose that in an assortment of 24 calculators there are 4 with defective switches. Draw with and…

A: given,total no.of calculators=24no.of defective switches=4

Q: 2. In a class, 60% of the students have brown hair, 30% have brown eyes, 10% have both brown hair…

A: Given,P(student has brown hair)=0.60P(student has brown eyes)=0.30P(student has both)=0.10

Q: One ball is drawn at random from a bag containing 2 red balls and 8 white balls. (Enter your…

A: Given that the bag containing 2 red and 8 white balls. One ball is drawn at random. The objective is…

Q: Both are face cards  B.) Both are aces  C.) Both are clubs

A: Number of face cards( Jack, Queen, King) is= 12 Number of Aces is= 4 Number of clubs is= 13 Number…

Q: 4. Agumball machine contains 60 gumballs of which 15 are yellow, 25 are pink, and 20 are blue. To…

A: It is given that the total gumballs are 60 of which 15 are yellow, 25 are pink and 20 are blue.10…

Q: Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store…

A: Given information: The total number of boxes on the shelf, N = 53 Out of these 53 boxes, the number…

Q: 5. Clarice has 7 new CDs; 3 are classical music and the rest are pop music. If she randomly grabs 3…

A: Clarice has 7 CD's in which 3 are of classical music and 4 are of pop music. She randomly selects 3…

Q: The probabllity that a palnting Job Is finishned in 2-5 days is 0.55, In 5-8 days is 0.76 and in 2-8…

A: Two events are said to be complementary when one event occurs if and only if the other does not. The…

Q: A PC manufacturer buys 38% of its chips from Japan, and the rest from the US. Of the Japanese chips,…

A: Given Data: P( Chips from japan)=0.38 P( Chips from US)=0.62   P( Defective chip from Japan)=0.017…

Q: 2. A man has 5 blue and 4 yellow balls in a bag. Without looking in the bag, he takes out a ball,…

A: Formula of probability : Probability =Number of favorable outcomes Toal outcomes

Q: Suppose we build a taco-making machine. But there is a fatal flaw in the machine, where for each…

A: Let X be that taco is toxic The probability that 5% of them are toxic , therefore p=0.05 therefore…

Q: Suppose that an employer plans to hire five people from a group of fourteen equally qualified…

A: Let X : number of minority candidates hired. X ~ bin (n, p) where, n = 5, p = 4/14= 0.285714, q =…

Q: First box contains 4 red balls and 2 green balls and the second box contains 4 green and two red…

A: Given          Box 2                          Box 1  Let event E1→Selecting box 1E2→Selecting box…

Q: A red ball and 9 white balls are in a box. If two balls are drawn, without replacement, what is the…

A: please see the explanation below

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.