Show that if B1, B2, and B3 are independent events then B1 and B2 U B3 are independent. Furthermore, also show that B1-B2 and B3 and independent.

Q: There is a 20 percent chance that a bidding fırm will get contract A and a 60 to percent chance they…

A: Two events are said to be independent provided the product of individual probabilities of both the…

Q: There is a 30 percent chance that a bidding fırm will get contract A and a 40 to percent chance they…

A:

Q: There is a 30 percent chance that a bidding fırm will get contract A and a 40 to percent chance they…

A: Let event A represent a bidding fırm will get contract A Let event B represent a bidding fırm will…

Q: Write a formula for MULTIPLICATION RULE FOR INDEPENDENT EVENT.

A: Multiplication theorem for probability of independent events  If A and B are two events with…

Q: Due to covid-19 the ministry of education decided to close the educational institutions. But in some…

A: Let X denote the number of institutions that remain open and it follows Poisson distribution with…

Q: Find the probability that both of the marbles drawn are red

A: It is given that Number of red marbles = 8 Number of white marbles = 13 Total number of marbles = 8…

Q: One bag contains 5 red balls and 4 black balls, and a second bag contains 4 red balls and 6 black…

A: Given Information: Bag one contains 5 red balls and 4 black balls. Bag two contains 4 red balls and…

Q: A doorman is holding 9 keys in which only 1 key will work on a room number 2A. What is the…

A: Given that  A doorman is holding 9 keys in which only 1 key will work on a room number 2A. Total…

Q: ONE BAG CONTAINS 5 WHITE BALLS AND 4 BLACK BALLS, AND A SECOND BAG CONTAINS 3 WHITE BALLS AND 6…

A: Given, First bag: W = 5 B = 4   Second Bag: W = 3 B = 6   To find, What is the probability that a…

Q: mong cats, 2% have a kidney disease . Of tests done, 82% can detect the disease when it is there,…

A: P(D') = 1- P(D) ___________________________________ I am using Bayes' theorem(Also provided Tree…

Q: You own 6 distinct pairs of shoes but keep all the individual shoes mixed up in the closet. Suppose…

A: If there are n mutually exclusive, exhaustive and equally likely outcomes of a random experiment and…

Q: Suppose A and B are two independent events. Prove A' and B are independent events. (Note: this is…

A: Given A and B are independent

Q: Suppose a telelvision company has 100 TVs in its stock with 8 defective ones. The company wants to…

A: There are total 100 TVs, among which 8 are defectives.A sample of 5 TVs are randomly selected.

Q: 4. Given the three events A. B. andC, what is the probability of their intersection AN BOC (ie.…

A: Basic probability

Q: Let A and B be two events with P (A) = 1/2 and P (B ^ c) = 1/4. The only thing we can say for sure…

A: It is given that A and B are two events. Therefore,

Q: There is a box which contains only blue, yellow and red marbles. Kyle randomly takes a marble from…

A: Given: A box contains only blue, yellow, and red marbles. Course of Actions: Kyle takes a marble and…

Q: One bag contains 4 white balls and 3 black balls, and a second bag contains 3 white balls and 5…

A: Ans - Given, One bag contains 4 white balls and 3 black balls, and a second bag contains 3 white…

Q: A bag contain 9 white and 1 black ball .3 of them are taken out a time from the bag .Find…

A: Given, A bag contains 9 white and 1 black ball . 3 of them are taken out a time from the bag . The…

Q: There is a 35 percent chance that a bidding fırm will get contract A and a 45 to percent chance they…

A: From the provided information, There is a 35 percent chance that a bidding firm will get contract A…

Q: If 4 married couples and 2 unmarried persons are arranged in a row, find the probability that no…

A: Let Ei = the ith couple sitting together where i = 1,2, 3,4 Then : P(E1) = 2×9!10! = 210=15 P(E1∩E2)…

Q: There is a 60 percent chance that a bidding fırm will get contract A and a 70 to percent chance they…

A: We have to find events are independent or not.

Q: Suppose you have 8 pairs of socks and 10 shirts in a drawer. Three of the pairs of socks are black…

A:

Q: Let A and B be two events with P (A) = 1/2 and P (B ^ c) = 1/4. The only thing we can say for sure…

A: # Given two events A and B such that  p(A)=1/2 & p(B^c)=1/4  then for Select one: to. A and B…

Q: Use the general multiplication rule to calculate probabilities of the fours possible outcomes.…

A: During one year Williams made 61% of her first serves. When she made her first serve, she won 76% of…

Q: Kat and Doug played 12 games of chess, of which 6 are won by Kat and 4 are won by Doug, and 2 end in…

A: Given : Total = 12games Kat wins 6, Doug wins 4, 2 are draw. They both Play 3 games

Q: A shipment consists of three identical boxes that contains the components. One box contains 1000…

A:

Q: Describe about the addition rule when Events Aren’t Mutually Exclusive.

A: Mutually exclusive events Two events are said to be mutually exclusive if they have no elements in…

Q: manufactured by 3 machines A, B and C. A produce twice as many items as B, and machines B and C…

A:

Q: What is the probility of no tails if two fair coins are tossed?

A: If Two fair coin is tossed Sample space is given by S = {(H,H),(H,T),(T,T),(T,H)} N(s) = 4 No of…

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

A:

Q: One coin is tossed twice. Case A is the first shot coming in tails, case B is the second shot coming…

A: It was stated that a coin is tossed twice. Case A is the first shot coming in tails. case B is the…

Q: A bag contains 3 white balls, 4 green balls and 5 red balls. Three balls are drawn from the bag…

A: Given,no.of white balls=3no.of green balls =4no.of red balls =5Total no.of balls =12

Q: one bag contains 4 white and 3 black and 2 nd bag contains 3 white and 5 black balls. One ball is…

A: bag 1 contains    4 white and 3 black  bag 2 contains  3 white and 5 black   One ball is drawn from…

Q: If two events are independent then their compliments are also independent. true False

A: Two events are said to be independent if occurrence of one event does not affect the occurrence of…

Q: Suppose a box contains 4 red and 4 blue balls. A ball is selected at random and removed, without…

A: We have to use Bayes theorem  In Bayes Theorem we find the posterior probability using the…