a)P(X=2|red)=P(2 heads out of 3 toss of fair coin)=3C2(0.5)2(0.5)1 =0.375
b)P(X=2|blue)=P(2 heads out of 3 toss of non-fair coin)=3C2(0.6)2(0.4)1 =0.432
c)
P(X=2)=P(red)*P(X=2|red)+P(blue)*P(X=2|blue)
=(2/5)*0.375+(3/5)*0.432=0.4092
d)
P(blue|X=2)=P(blue)*P(X=2|blue)/P(X=2)=(3/5)*0.432/0.4092=0.6334
Problem 3. A ball is taken at random from an urn containing 2 red balls and...
A ball is taken at random from an urn containing 2 red balls and 3 blue balls. If the ball is red a fair coin is tossed three times. If the ball is blue non-fair coin is tossed three times; for this second coin the probability of heads is .6. In either case we count the number of heads in the three tosses and call that number X. (a) Compute the conditional probability that X-2 if it is known that...
Consider an urn containing 6 red balls and 3 blue balls from which 3 balls are selected without replacement. What is the probability of selecting a red ball, if you select exactly one blue ball?
both abcd thanks ii) An urn contains 200 red balls and 400 blue balls. A player performs the ollowing experiment 180 times: choose a ball from the urn at random record its colour and put it back in the urn. Let X be the number of times a red ball was selected a) Write down, but do not evaluate, an expression for the probability that X b) Calculate the mean and variance of X c) Use a normal approximation to...
Consider an urn initially containing N є N balls. For n E Z+, let Xn be the number of balls in the urn after performing the following procedure n times. If the urn is non-empty, one of the balls is removed at random. A fair coin is flipped, and if the coin lands tails then the ball is returned to the urn. If the coin lands heads, the ball is not returned. If the urn is empty, then the coin...
In an urn, there are 3 blue balls and 2 red balls. A ball is selected at random without replacement. Regardless of what color the first ball was, a blue ball is added to the urn (so there are a total of 5 balls in the urn now). Then a second ball is selected from the urn. a) What is the chance that the second ball selected from the urn is blue? b) Given that the second ball is blue,...
In an urn, there are 3 blue balls and 2 red balls. A ball is selected at random without replacement. Regardless of what color the first ball was, a blue ball is added to the urn (so there are a total of 5 balls in the urn now). Then a second ball is selected from the urn. a) What is the chance that the second ball selected from the urn is blue? b) Given that the second ball is blue,...
Urn One has 11 red balls and 8 blue balls. Urn Two has 10 red balls and 5 blue balls. An urn is selected at random and then a ball is selected from the selected urn at random. What is the probability that the ball selected is blue? State your answer to three places of decimal. Your Answer:
An urn contains 3 red balls, 2 blue balls, and 5 white balls. A ball is selected and its color noted. Then it is replaced. A second ball is selected and its color noted. Find the probability of: Selecting 2 blue balls (round to 4 decimal places)
4. Suppose urn 11 is filled with 60% green balls and 40% red balls, and urn T is filled with 40% green balls and 60% red balls. Someone will flip a coin and then select a ball from urn H or T depending on whether the coin lands heads or tails, respectively. Let X be 1 or 0 if the coin lands heads or tails, and let Y be 1 or 0 if the ball is green or red (a)...
Suppose that there is a white urn containing two white balls and three red balls and there is a red urn containing three white balls and four red balls. An experiment consists of selecting at random a ball from the white urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball. Find the probability that the second ball is red. The probability of the second ball being...