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

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
It did not answer the questions since it was asking What is the probability that Bill was accepted at College Y given that he was accepted at College X?
For the experiment of rolling an ordinary pair of dice, find the probability that the sum will be 10 or 3. (You may want to use a table showing the sum for each of the 36 equally likely outcomes.) The probability that the sum of the pair of dice is 10 or 3 is (Simplify your answer.)
Sean flipped a coin 100 times and got heads 42 times. He concludes that the probability of g heads on a flip of his coin is 0.42. Which method did Sean use?
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?
Frank noticed that his mother will serve salad with dinner 78% of the nights, will serve potatoes with dinner 30% of the nights and will serve both 14% of the nights. The probability, to the nearest hundredth, that Frank's mother will serve salad or potatoes is
At races, your horse, White Rum, has a probability of 1/20 of coming 1st, 1/10 of coming 2nd and a probability of ¼ in coming 3rd. First place pays $5,000 to the winner, second place $4,000 and third place $1,350. Hence, is it worth entering the race if it costs $1050?
On cloudy days, Lucy has ramen for lunch with probability 0.4.On non-cloudy days, she has ramen with probability 0.2.There's a probability of 0.3 that it'll be cloudy tomorrow.What's the probability that she eats ramen tomorrow?
Ken has applied to both FSU and the UGA. He thinks the probability that FSU will admit him is 0.4, the probability that UGA will admit him is 0.5, and the probability that both will admit him is 0.1. What is the probability that Ken will not get into either school?
Friskie is having her fifth litter. The prior litters have either been three normal pups or two normal pups and a runt. Assume the probability of either outcome is 50%.
Q18. A biased coin is flipped 6 times. In a single flip of the coin, the probability of heads is 1/3 and the probability of tails is 2/3. The outcomes of the coin flips are mutually independent. What is the probability the first two flips come up heads and the rest of the flips come up tails? (Round to four decimal places.)