1.a person selects a card from a deck .it is a red card ,he wns 1$.if it is black face card between or including 2 and 10,he wins $5.if it is black face card,he wins $10 and if it is black ace,he wins $100.find the expectation of the game is to be fair?
2.if 30% of all commuters ride the train to work,find the probability that if 10 workers are selected,5 will ride the train
3.if 10 % of the people who are given a certain drug experience dizziness,find these probabilities for a sample of 15 people who take the drug
4.a club has 225 members.if there is a 70% attendance rate per meeting ,find the mean,variance,and standard deviation of the number of people who pass will be present at each meeting
5.if 4% of the populationcarries a certain genetic trait,find the probability that in a sampleof 100 people,there are exactly 8 people who have the trait .assume the distibutionis approximately poisson
6.a board of directors consist of seven men and five women.if a slate of three officers is selected find these probabilities
7.three out of four american adults aunder age 35 have eaten pizza for breakfat.if random sample of 20 adults under age 35 is selected,find the probability that exactly 16 have eaten pizza for breakfast
8.one out of americans over age 55 has eaten pizza for breakfast.if a sample of 10 americans over age 55 is selcted at random,find the probability that at most 3 have eaten pizza for breakfast
9.of the 50 automobiles in a used-car lot,10 sre white .if five automobiles are selected to be sold at an auction,find the probability that exactly two will be white
10.(opt)if five cards are drawn from a deck ,find the probability that two will be hearts
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1. To find the expectation of the game, we need to calculate the expected value of the winnings for each possible outcome, and then sum them up.
- There are 26 red cards in a deck and a person wins $1 if they select a red card. So the expected value for this outcome is (26/52) * $1 = $0.50.
- There are 20 black face cards between 2 and 10 in a deck and a person wins $5 if they select one. So the expected value for this outcome is (20/52) * $5 = $1.92.
- There are 3 black face cards (Jack, Queen, King) and a person wins $10 if they select one. So the expected value for this outcome is (3/52) * $10 = $0.58.
- There is only 1 black Ace in a deck and a person wins $100 if they select it. So the expected value for this outcome is (1/52) * $100 = $1.92.
Now, let's sum up the expected values:
$0.50 + $1.92 + $0.58 + $1.92 = $4.92
Therefore, the expectation of the game is $4.92.
2. If 30% of all commuters ride the train to work, the probability that 5 out of 10 workers selected ride the train can be calculated using the binomial probability formula:
P(5 out of 10 ride the train) = C(10, 5) * (0.30)^5 * (0.70)^5
You can plug this into a calculator or use a statistical software to find the probability.
3. Similarly, if 10% of the people who take a certain drug experience dizziness, the probability that a sample of 15 people who take the drug will have a specific number of people experiencing dizziness can be calculated using the binomial probability formula.
4. If a club has 225 members and there is a 70% attendance rate per meeting, the mean (expected value), variance, and standard deviation of the number of people who will be present at each meeting can be calculated using the formulas for a binomial distribution.
5. If 4% of the population carries a certain genetic trait, the probability that in a sample of 100 people, exactly 8 people have the trait can be calculated using the Poisson distribution formula.
6. If a board of directors consists of seven men and five women, and a slate of three officers is selected, the probabilities of selecting a specific number of men or women as officers can be calculated using the binomial probability formula.
7. If three out of four American adults under age 35 have eaten pizza for breakfast, the probability that exactly 16 out of 20 adults in a random sample under age 35 have eaten pizza for breakfast can be calculated using the binomial probability formula.
8. If one out of Americans over age 55 has eaten pizza for breakfast, the probability that at most 3 out of a sample of 10 Americans over age 55 have eaten pizza for breakfast can be calculated using the binomial probability formula.
9. If there are 10 white automobiles out of 50 in a used-car lot, the probability that exactly two out of a sample of five automobiles selected to be sold at an auction are white can be calculated using the hypergeometric distribution formula.
10. If five cards are drawn from a deck, the probability that exactly two of them are hearts can be calculated using the hypergeometric distribution formula.