1) If a \(7\) card hand is dealt from a standard deck of \(52\) cards, find each probability to the nearest thousandth.
a) P(\(4\) diamonds and \(3\) hearts)
b) P(\(4\) Kings)
c) P(majority red)
d) P(at most \(3\) clubs)
2) An Algebra \(2\) class has \(14\) male students and \(17\) female students. If the teacher wants to form a committee of \(6\) people, what is the probability, to the nearest thousandth, that \(4\) males and \(2\) females will be chosen?
3) A humane society has \(75\) dogs for adoption. \(55\) of the dogs are mix breeds and \(7\) dogs have blue eyes. There is a \(5\%\) chance that a mix breed will have blue eyes. What is the probability of picking a dog that is a mix breed or has blue eyes?
4) A group of \(7\) people is to be formed from a group of \(11\) men and \(8\) women. What is the probability that the committee will have at least \(5\) women?
5) Nick L. purchased several songs. \(45.7\%\) of the songs were country songs. Of the \(1,376\) songs Nick has, \(432\) were over \(4\) minutes long. If \(13.5\%\) of the songs that are over \(4\) minutes long are country songs, what is the probability that a randomly selected song will be country or over \(4\) minutes long?
6) Two skittles are drawn at random from a bag containing \(7\) red, \(4\) purple, and \(3\) yellow skittles. Find each probability to the nearest thousandth.
a) P(\(2\) skittles of the same color)
b) P(\(2\) skittles of different colors)
c) P(at least one yellow skittle)
7) You pay \(\$0.25\) to spin the pictured spinner. If you spin blue, you don't win anything. If you spin red, you get your \(\$0.25\) back and if you spin orange, then you win \(\$0.30\). What is your mathematically expected payoff?
8) A farmer produces eggs at a cost of \(\$0.80\) per dozen. He sells his eggs to a local grocer for \(\$1.50\) per dozen. Eggs are checked by quality control with the follow restrictions. If two eggs are randomly selected from \(4\) dozen eggs, and there is one bad egg, the farmer loses his \(\$0.80\) productions costs. If two eggs are bad, the farmer loses his production costs and he has to pay a \(\$100\) fine. What is the mathematical expectation of the farmer's profit if out of the 4 dozen eggs, there is exactly one bad egg?
Solution Bank
a) P(\(4\) diamonds and \(3\) hearts)
b) P(\(4\) Kings)
c) P(majority red)
d) P(at most \(3\) clubs)
2) An Algebra \(2\) class has \(14\) male students and \(17\) female students. If the teacher wants to form a committee of \(6\) people, what is the probability, to the nearest thousandth, that \(4\) males and \(2\) females will be chosen?
3) A humane society has \(75\) dogs for adoption. \(55\) of the dogs are mix breeds and \(7\) dogs have blue eyes. There is a \(5\%\) chance that a mix breed will have blue eyes. What is the probability of picking a dog that is a mix breed or has blue eyes?
4) A group of \(7\) people is to be formed from a group of \(11\) men and \(8\) women. What is the probability that the committee will have at least \(5\) women?
5) Nick L. purchased several songs. \(45.7\%\) of the songs were country songs. Of the \(1,376\) songs Nick has, \(432\) were over \(4\) minutes long. If \(13.5\%\) of the songs that are over \(4\) minutes long are country songs, what is the probability that a randomly selected song will be country or over \(4\) minutes long?
6) Two skittles are drawn at random from a bag containing \(7\) red, \(4\) purple, and \(3\) yellow skittles. Find each probability to the nearest thousandth.
a) P(\(2\) skittles of the same color)
b) P(\(2\) skittles of different colors)
c) P(at least one yellow skittle)
7) You pay \(\$0.25\) to spin the pictured spinner. If you spin blue, you don't win anything. If you spin red, you get your \(\$0.25\) back and if you spin orange, then you win \(\$0.30\). What is your mathematically expected payoff?
8) A farmer produces eggs at a cost of \(\$0.80\) per dozen. He sells his eggs to a local grocer for \(\$1.50\) per dozen. Eggs are checked by quality control with the follow restrictions. If two eggs are randomly selected from \(4\) dozen eggs, and there is one bad egg, the farmer loses his \(\$0.80\) productions costs. If two eggs are bad, the farmer loses his production costs and he has to pay a \(\$100\) fine. What is the mathematical expectation of the farmer's profit if out of the 4 dozen eggs, there is exactly one bad egg?
Solution Bank