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Elza [17]
4 years ago
15

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.
Mathematics
1 answer:
dolphi86 [110]4 years ago
5 0

Answer:

(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.

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2 years ago
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Step-by-step explanation:

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6 0
3 years ago
Read 2 more answers
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qaws [65]

Answer:

Part A = D

Part B = 5 and 50

Step-by-step explanation:

Part A:

area = 5*4x = 20x

so, 100 \leq 20x \leq  1000

Part B:

to leave it only by x, you divide both sides by 20

100/20 = 5, 1000/20 = 50

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7 0
3 years ago
The line x+ 2y = 9 intersects the curve xy + 18 = 0 at the points A and B. Find the coordinates of A and B.
victus00 [196]
Subtracting the second equation by 18 on both sides, we have xy=-18. Next, we divide both sides by x to get y=-18/x  Plugging that into the first equation, we have x+2(-18/x)=9. Multiplying both sides by x, we get x^2-36=9x. After that, we subtract both sides by 9x to get x^2-9x-36=0. Finding 2 numbers that add up to -9 but multiply to -36, we do a bit of guess and check to find the answers to be -12 and 3. Factoring it, we get 
x^2-12x+3x-36=x(x-12)+3(x-12)=(x+3)(x-12). To find the x values, we have to find out when 0=(x+3)(x-12). This is simple as when you multiply 0 with anything, it is 0. Therefore, x=-3 and 12. Plugging those into x=-18/y, we get x=-18/y and by multiplying y to both sides, we get xy=-18 and then  we can divide both sides by x to get -18/x=y. Plugging -3 in, we get -18/-3=6 and by plugging 12 in we get -18/12=-1.5. Therefore, our points are (-3,6) and (12, -1.5)
6 0
3 years ago
7.
snow_tiger [21]

Answer:

Range is 18.

Step-by-step explanation:

Range can be calculated by subtracting the smallest value of the data set from the largest value of the data set.

The values are:

13, 17, 18, 15, 12, 21, 10, 6, 8, 11, 3

Largest Value in this data set:  21

Smallest Value in this data set: 3

Range = Largest Value - Smallest Value

Range = 21 - 3

Range = 18

6 0
3 years ago
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