I would like to know why the approach to the problem below is wrong: When coin A is flipped, it lands on heads with probability 0.4. When coin B is flipped, it lands on heads with probability 0.7. One of these coins is randomly chosen and flipped 10 times. Given that the first of these 10 flips lands heads, what is the conditional probability that exactly 7 of the 10 flips land on heads? Wrong approach: X: number of times the coin lands on heads H: first of these 10 flips lands heads A: coin A is chosen B: coin B is chosen P(X=7|H) = P(X=7, A|H) + P(X=7, B|H) = 9C6 x (0.4^6) x (0.6^3) x 0.5 + 9C6 x (0.7^6) x (0.3^3) x 0.5 = 0.1706 However, the correct answer is 0.1968.

I would like to know why the approach to the problem below is wrong: When coin A is flipped, it lands on heads with probability 0.4. When coin B is flipped, it lands on heads with probability 0.7. One of these coins is randomly chosen and flipped 10 times. Given that the first of these 10 flips lands heads, what is the conditional probability that exactly 7 of the 10 flips land on heads? Wrong approach: X: number of times the coin lands on heads H: first of these 10 flips lands heads A: coin A is chosen B: coin B is chosen P(X=7|H) = P(X=7, A|H) + P(X=7, B|H) = 9C6 x (0.4^6) x (0.6^3) x 0.5 + 9C6 x (0.7^6) x (0.3^3) x 0.5 = 0.1706 However, the correct answer is 0.1968.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

I need the answer as soon as possible
Find the conditional probability of the given event when two fair dice (one red and one green) are rolled. The red one is 2, given that the green one is 2. X 0.17
christmas tree lights are used not only for christmas trees,but sometimes to decorate college dorm rooms. suppose that a string has 20 light bulbs. these lights are all wired in series, so that if one light bulbs fails,the whole string fails. the probability that any one light fails is 0.02.eah of the individual lights are independent of each other. what is the probability that the string will not fail ?
On cloudy days, Lucy has ramen for lunch with probability 0.4. On non-cloudy days, she has ramen with probability 0.2. We know she's having ramen tomorrow. What's the probability that it's cloudy tomorrow?
A researcher is selecting lab rats for her experiment. She assigns each rat a number and picks numbers out of a hat while blindfolded. The pool of rats from which she is drawing participants is composed of the following: 23 male albino rats 21 male spotted rats 35 female albino rats 11 female spotted rats If she reaches into the hat once, what is the probability of choosing a female rat or an albino rat? Give your answer as a decimal rounded to 4 decimal places.
On Mr. Casper's debate team at Thunderbird High School, 20% of the members are Sophomores, 35% are Juniors and 45% are Seniors. A team member is selected randomly to give the closing argument for the team. If a sophomore gives the closing argument, the team has a probability of 0.25 of winning the debate. If a junior gives the closing argument, the probability of winning is 0.6. If a senior closes, the probability of winning is 0.85. (a) Find the probability that the team wins the debate. b sketch a tree diagram to model this process
On any given morning here at Chabot College, coffee is brewed in the Science and Math Division workroom by one of two faculty members, depending on who arrives first at work. Instructor Yest arrives first 75% of the time. Instructor Kelly arrives first the remaining mornings. The probability that the coffee is brewed strong when brewed by Instructor Yest is 0.2. The probability that the coffee is brewed strong when brewed by Instructor Kelly is 0.9, as Instructor Kelly likes her coffee strong! Given the coffee is strong on a randomly selected morning, what is the probability that is was brewed by Instructor Yest?
The management of the large department store in Example B.1 must determine whether more training is neededfor the customer service clerk. The clerk at the customer service desk can serve an average of three customersper hour. What is the probability that a customer will require 10 minutes or less of service?
Suppose you roll the dice repeatedly, and you will keep flipping it until you observe two total sixes, and then stop. What is the probability that it takes exactly 4 rolls to get your two sixes?
Jeri is listening to the songs on a new CD in random order. She will listen to two different songs, and will buy the CD if she likes both of them. Assume that there are 10 songs on the CD and that she would like 5 of them. Before she had listened to any of the songs on the CD, what would have been the probability that she would buy the CD? Hint: To find this probability, first find the number of combinations of 2 out of the 5 songs that she likes (how many different combinations of 2 out of the 5 songs are there?). Then find the number of combinations of 2 out of the 10 songs on the CD (how many different combinations of 2 songs can she pick from the CD?). Take the number of combinations of the 5 songs she likes and divide that by the number of combinations of the 10 songs.. Question 7 options: A. 10/45 or 22% B. 10/120 or 8.3% C. 4/9 or 44% D. 45/10 or 450%