Probability related questions
Q-1 A box contains 500 envelopes of which 75 contain $100 in cash, 150 contain $25 , and 275 contain $10. An envelope may be purchased for $25. What is the sample space for the different amounts of money? Assign probabilities to the sample points and then find the probability that the first envelope purchased contains less than $100.
Q-2 Suppose that in a senior college class of 500 students it is found that 210 smoke, 258 drink alcoholic beverages, 216 eat between meals, 122 smoke and drink alcoholic beverages, 83 eat between meals, and drink alcoholic beverages, 97 smoke and eat between meals, and 52 engage in all three of these bad health practices. If a member of this senior class is selected at random, find the probability that the student.
(a) smokes but does not drink alcoholic beverages;
(b) eats between meals and drinks alcoholic beverages but does not smoke;
(c) neither smokes nor eats between meals.
Q-3 The probability that and American industry will locate in Munich is 0.7, the probability that it will locate in Brussels is 0.4, and the probability that it will locate in either Munich and Brussels or both is 0.8. What is the probability that the industry will locate
(a) In both cities?
(b) In neither city?
Q-4 From past experiences a stockbroker believes that under present economic conditions a customer will invest in tax-free bonds with a probability of 0.6, will invest in mutual funds with a probability of 0.3, and will invest in both tax-free bonds and mutual funds with a probability of 0.15. At this time, find the probability that a customer will invest.
(a) In either tax-free bonds or mutual funds;
(b) In neither tax-free bonds nor mutual funds.
Q-5 If a letter is chosen at random from the English alphabet, find the probability that the letter
(a) Is a vowel exclusive of y;
(b) Is listed somewhere a head of the letter j;
(c) Is listed somewhere after the letter g.
Q-6 An automobile manufacturer is concerned about a possible recall of their best-selling four-dour sedan. If there were a recall, there is 0.25 probablity that a defect is in the brake system, 0.18 in the transmission, 0.17 in the fuel system, and 0.40 in some other area.
Q-7 If each coded item in a catalog begins with 3 distinct letters followed by 4 distinct nonzero digits,find the probability of randomly selecting one of these coded items with the first letter a vowel and the last digit even.
Q-8 Two cards are drawn in succession from a deck without replacement. What is the probability that both cards are greater than 2 and less than 8?
Q-9 If 3 books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that
(a) The dictionary is selected?
(b) 2 novels and 1 book of poems are selected?
Q-10 In a poker hand consisting of 5 cards, find the probability of holding
(a) 3 acres;
(b) 4 hearts and 1 club.
Q-11 In a game of yahtzee, where 5 dice are tossed simultaneously, find the probability of getting 4 of a kind.
Q-12 In a high school graduating class of 100 students, 54 studied mathematics, 69 studied history, and 35 studied both mathematics and history. If one of these students is selected at random, find the probability that
a. The student took mathematics or history;
b. The students did not take either of these subjects;
c. The student took history but not mathematics.
Q-13 Dom`s Pizza Company uses taste testing and ststistical analysisof the data prior to marketing any new product. Consider a study involving three types of crusts (thin, thin with garlic and oregano, and thin with bits of cheese). They are also studying three sauces, (standard, a new sauce with more garlic, and a new sauce with fresh basil).
a) How many combinations of crust and sauce are involved?
b) What is the probability that a judge will get a plain thin crust with a standard sauce for his first taste test?
