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APA
Subject:
Mathematics & Economics
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Math Problem
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English (U.S.)
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Show your work in the problems. Solving Probabilities.

Math Problem Instructions:

Show your work in the problems.
1. In families with four children, you’re interested in the probabilities for the different possible numbers of girls in a family. Using theoretical probability (assume girls and boys are equally likely), compile a five-column table with the headings “0” through “4,” for the five possible numbers of girl children in a four-child family. Then, using “G” for girls and “B” for boys, list under each heading the various birth-order ways of achieving that number of girls in a family.
Then, use your table to calculate the following probabilities:
a. The probability of 1 girl
b. The probability of 2 girls
c. The probability of 4 girls
d. The probability the third child born is a girl
2. As pictured in Figure 6.11 of your textbook, a roulette wheel has 38 numbers: 18 odd black numbers from 1 to 35, 18 even red numbers from 2 to 36, and the two green numbers 0 and 00. Using theoretical probability, calculate the following:
a. The probability of spinning a green number
b. The probability of spinning a number greater than 30
c. The probability of spinning a red number less than 10
d. The probability of spinning an even black number
e. The expected total of green numbers in 57,000 spins
3. In a nationwide polls of 1,500 randomly selected U.S. residents, 77% said that they liked pizza. In a poll of 1,500 randomly selected U.S. residents one month later, 75% responded that they liked pizza.
a. Does the polling evidence support the claim that pizza declined in popularity over the month between polls? Explain why or why not.
b. Using statistical terminology, precisely identify the population parameter the two polls were attempting to measure. How does a parameter differ from a statistic?
c. Based on the two polls, what would you say to someone who guessed that the population parameter the polls are trying to measure is really only 50%?
4. Eleven people have eleven different favorite numbers from 2 to 12. They all agree to participate in a 10,000-roll dice game where they bet $1 on their favorite number for each roll of two standard (fair) dice. A donor kicks in an extra dollar every round, so the payoff if your number comes up is $12.
a. Assuming everyone bets on all 10,000 rounds, what is the expected value for a person who has number 7? (Show your calculations.)
b. Assuming everyone bets on all 10,000 rounds, what is the expected value for a person who has number 2? (Show your calculations.)

Math Problem Sample Content Preview:

Solving Probabilities
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Solving Probabilities
In families with four children, you’re interested in the probabilities for the different possible numbers of girls in a family. Using theoretical probability (assume girls and boys are equally likely), compile a five-column table with the headings “0” through “4,” for the five possible numbers of girl children in a four-child family. Then, using “G” for girls and “B” for boys, list under each heading the various birth-order ways of achieving that number of girls in a family.
Table showing possible probabilities of the number of girl children
012341
BBBB
P=1/16
=0.0625
=6.25%4
GBBB
BGBB
BBGB
BBBG
P=4/16
=0.25
=25%6
GGBB
GBGB
BGGB
BBGG
GBBG
BGBG
P=6/16
=0.375
=37.5%4
GGGB
BGGG
GGBG
GBGG
P=4/16
=0.25
=25%1
GGGG
P=1/16
=0.0625
=6.25%
Total Probabilities = 2 x 2 x 2 x 2 = 16
GGGG, GGGB, GGBG, GBGG, BGGG, GGBB, GBGB, BGGB, BGBG, BBGG, GBBB, BGBB, BBGB, BBBG, BBBB, GBBG
Then, use your table to calculate the following probabilities:
The probability of 1 girl
P(GBBB, BGBB, BBGB, BBBG)
Probability of 1 girl = 4/16 = 0.25 = 25%
The probability of 2 girls
P(GGBB, GBGB, BGGB, BBGG, GBBG, BGBG)
Probability of 2 girls = 6/16 = 0.375 = 37.5%
The probability of 4 girls
P(GGGG)
Probability of 4 girls = 1/16 = 0.0625 = 6.25%
The probability the third child born is a girl
P(BBGB, GBGB, BGGB, BBGG, GGGB, BGGG, GBGG, GGGG)
Probability of 3rd child being a girl = 8/16 = 0.5 = 50%
As pictured in Figure 6.11 of your textbook, a roulette wheel has 38 numbers: 18 odd black numbers from 1 to 35, 18 even red numbers from 2 to 36, and the two green numbers 0 and 00. Using theoretical probability, calculate the following:
The probability of spinning a green number
Probability of spinning a green number, P(0,00) = 2/38
= 0.05263 = 5.26%
The probability of spinning a number greater than 30
Probability of spinning a number > 30, P(31,32,33,34,35,36,37,38)
= 8/38 = 0.2105
= 21.05%
The probability of spinning a red number less than 10
Probability of spinning red number < 10, P(2,4,6,8)
= 4/38 = 0.1052
= 10.52%
The probability of spinning an even black number
Probability of spinning even black number = 0/38 = 0%
Since all black numbers are odd
The expected total of green numbers in 57,000 spins
Expected green numbers in 57,000 spins = E(X)
Since probability of spinning green numbers, P(0,00) = 2/38 = 1/19
Then E(X) = n Ч p, where n = 57,000 and p = 1/19
Thus E(X) = 57,000Ч1/19
E(X) = 3,000
In a nationwide poll of 1,500 randomly selected U.S. residents, 77% said that they liked pizza. In a poll of 1,500 randomly selected U.S. residents one month later, 75% responded that they liked pizza.
From the given data: sample size n1 = 1,500
First Poll, ...
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