![gungamer720](/avatars/4588.jpg)
gungamer720
15.04.2020 •
Mathematics
Ben and Allison each decide to wager 1 unit against the other person on flips of an unfair coin, with probability 0.6 of landing head, until one of them runs out of money. When the flip lands on head, Ben wins 1 unit from Allison; and when the coin lands on tail, Allison wins 1 from Ben. At the start of the contest, Ben has 30 units and Allison has 45 units. Find (a) the average number of flips needed until Ben is eventually broke, (b) the average number of flips needed until Allison is eventually broke, and (c) the average number of flips needed until either Ben or Allison is eventually broke.
Solved
Show answers
More tips
- L Leisure and Entertainment What Movies You Should Watch: A Guideline to Make the Right Decision...
- F Family and Home How to Choose a Baby Stroller: Tips from Experienced Parents...
- H Health and Medicine 5 Simple Steps to Quit Smoking for Good...
- C Computers and Internet How to Download Videos from YouTube? Simple Steps to Download Any Content...
- H Health and Medicine What is the Normal Blood Sugar Level in a Healthy Person?...
- S Style and Beauty How to Get Rid of Acne: Scientifically Proven Methods...
- L Leisure and Entertainment How to Choose the Perfect Gift for Men on February 23rd?...
- C Computers and Internet How to Delete Your Account on Odnoklassniki...
- H Health and Medicine 10 Simple and Effective Tips on How to Lose Weight in a Week...
- F Food and Cooking What s the Best Rice for Cooking Plov?...
Answers on questions: Mathematics
- M Mathematics Whey y varies directly with x. Write an equation for the direct variation then find the value. Note: Leave improper fractions .. improper! find y when x=3, if y=-4 when...
- M Mathematics Pls help asap due tmr...
- M Mathematics Tessa owns 5/8 of an acre of farmland. She grows beets on 1/2 of the land. On how many acres of land does Tessa grow beets? Write your answer as a fraction or as a whole...
- M Mathematics Sean organized his rubber duck collection in two rows on a shelf in his room. He put 14 rubber ducks in one row and the rest in a second row. If Sean has 29 rubber ducks...
- M Mathematics Write and solve an inequality to find the possible values of x if the minimum area of the trapezoid is to be at least 45 square feet. (2x + 3) feet 9 feet (4x - 6) feet...
- M Mathematics 4. Mr. Perez s science students conducted a wildlife count in the local forest. The results of their count are shown in the table. 25 Squirrel Rabbit 10 A. Find the angle...
- M Mathematics Find the value of x. Area of circle = 25(pi) radius = x + 3...
- M Mathematics Use finite differences to determine the degree of the polynomial function that fits the data Then use technology to find the polynomial function (-4,-317), (-3,-37). (-...
- M Mathematics Question 12 (5 points) The function f(x) = -1/3x2 is shifted down one unit. Which of the following function equations...
- M Mathematics At the coffee shop, the ratio of cups of coffee sold to muffins was 2:7. If the shop sold 84 muffins, how many cups of coffee did the shop sell?...
Ответ:
(A) 75 flips
(B) 75 flips
(C) 75 flips
Step-by-step explanation:
Normally, the coin will have to land on tail 30 sure times (Allison will win 30 units from Ben) before Ben will be broke.
This does not mean that the first 30 flips will favour Allison (that Ben will get broke in the first 30 flips) hence we use the probability of tail to ascertain how many times the coin will be flipped until 30 tails are gotten. And for each sure tail, the coin will be tossed/flipped a number of times before the probability of tail will be one.
Also note that the coin used for this experiment is a biased or unfair coin. That is, both sides - head and tail - don't have an equal probability of occurrence which is 1/2 or 0.5
Same method applies for Head. The coin will have to land on Head 45 sure times (where in each time, probability of head occurring is 1) before Allison will be broke.
(A) Average number of flips needed until Ben is broke
This is equal to the average number of flips it takes for a tail to be gotten for sure X the number of units Ben will lose until he's broke.
The number of flips it takes to get a tail for sure is 2.5 flips.
How? 3 flips will get p(T) = 1.2
Hence 2.5 flips will get p(T) = 1
And that is when Ben loses a unit of his money
Now, if in 2.5 flips we have a tail, it will take X flips for us to get 30 tails
Cross multiply:
X = (2.5×30) / 1 = 75 flips
(B) Using the same cross multiplication method, we find that it takes 1.667 flips for Ben to win 1 unit of Allison's money because in 2 flips, the probability of head is 1.2, which is above 1.
So since it takes 1.667 for Allison to lose 1 unit of his money, it will take X flips for Allison to lose 45 units of his money
Cross multiply:
X = (45×1.667)/1 = 75 flips
(C) We would have had to use a formula for this one but there is no need, since it takes the same 75 flips for either Ben or Allison to get broke.
Ответ:
good luck
Step-by-step explanation: