Jaclyn has $120 saved and earns $40 each month in allowance. Pedro has $180 saved and earns $20 a month in allowance. If they bo
th save their entire allowances, how long will it take before Jaclyn and Pedro have saved the same amount of money?
1 answer:
First, let's make an equation as to how to find how much money they have altogether:
(M stands for the # of month)
Jaclyn: 120 + 40m
Pedro: 180 + 20m
So let's plug-in 1 for m (1 will stand for 1 month)
Jaclyn: 120 + 40 * 1 = 160
Pedro: 180 + 20 * 1 = 200
I made a table depicting how much they'll make for the next 5 months (attached below). According to that, on month 3, they will have made the same amount of money (or $240).
So they will have the same amount of money in 3 months. Hope this helps! :)
(M stands for the # of month)
Jaclyn: 120 + 40m
Pedro: 180 + 20m
So let's plug-in 1 for m (1 will stand for 1 month)
Jaclyn: 120 + 40 * 1 = 160
Pedro: 180 + 20 * 1 = 200
I made a table depicting how much they'll make for the next 5 months (attached below). According to that, on month 3, they will have made the same amount of money (or $240).
So they will have the same amount of money in 3 months. Hope this helps! :)
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Answer:
(a) The expected value of the prize for one play of Instant Lotto is $3.50.
(b) The probability that the visitor wins some prize at least twice in the 20 free plays is 0.2641.
(c) The probability that a randomly selected day has at least 1000 people play Instant Lotto is 0.2579.
Step-by-step explanation:
(a)
The probability distribution of the monetary prizes that can be won at the game called Instant Lotto is:
<em>X</em> P (<em>X</em> = <em>x</em>)
$10 0.05
$15 0.04
$30 0.03
$50 0.01
$1000 0.001
$0 0.869
___________
Total = 1.000
Compute the expected value of the prize for one play of Instant Lotto as follows:
Thus, the expected value of the prize for one play of Instant Lotto is $3.50.
(b)
Let <em>X</em> = number of times a visitor wins some prize.
A visitor to the casino is given <em>n</em> = 20 free plays of Instant Lotto.
The probability that a visitor wins at any of the 20 free plays is, <em>p</em> = 1/20 = 0.05.
The event of a visitor winning at a random free play is independent of the others.
The random variable <em>X</em> follows Binomial distribution with parameters <em>n</em> = 20 and <em>p</em> = 0.05.
Compute the probability that the visitor wins some prize at least twice in the 20 free plays as follows:
P (X ≥ 2) = 1 - P (X < 2)
= 1 - P (X = 0) - P (X = 1)
Thus, the probability that the visitor wins some prize at least twice in the 20 free plays is 0.2641.
(c)
Let <em>X</em> = number of people who play Instant Lotto each day.
The random variable <em>X</em> is normally distributed with a mean, <em>μ</em> = 800 people and a standard deviation, <em>μ</em> = 310 people.
Compute the probability that a randomly selected day has at least 1000 people play Instant Lotto as follows:
Apply continuity correction:
P (X ≥ 1000) = P (X > 1000 + 0.50)
= P (X > 1000.50)
Thus, the probability that a randomly selected day has at least 1000 people play Instant Lotto is 0.2579.