<1> A card is drawn from an ordinary deck and we are told that it is red. What is the probability that the card is an 8 ? (1/13)
<2> Farmer Fran sends out 10,000 cartons of eggs every day. Two inspectors independently glance at each carton to see if there are any broken eggs, and each has 0.8 probability of noticing when a carton has cracked eggs. What is the probability that a carton with broken eggs will be noticed by at least one inspector? (0.96)
<3> One bag contains 6 white balls and 4 black balls, and a second bag contains 5 white balls and 4 black balls. One ball is drawn at random from the first bag and is placed unseen in the second bag. a) What is the probability that a ball now drawn from the second bag is black? (11/25). b) If the ball from the second bag is black, what is the probability that the ball from the first bag was white? (6/11)
<4> A blood disease is found in 2% of the persons in a certain population. A new blood test will correctly identify 96% of the persons with the disease and 94% of the persons without the disease. (a) What is the probability that a person who is called positive by the blood test actually has the disease? (0.246). (b) What is the probability that a person who is called negative by the blood test actually does not have the disease? (0.999)
<5> A pair of dice is thrown. If it is known that one die shows a 4, what is the probability that a) the other die shows a 5? (2/11) b) the total of both is greater than 7? (5/11)
<6> A town has 2 fire engines operating independently. The probability that a specific fire engine is available when needed is 0.92. a) What is the probability that at least one is available when needed? b) What is the probability that both are available when needed? (0.9936; 0.8464)
<7> A shipment of 7 TV sets contains 2 defective sets. A motel makes a random purchase of 3 sets. If X is the number of defective sets purchased by the motel, find the probability distribution of X and the mean of X.(10/35, 20/35, 5/35; 6/7)
<8> In a gambling game a man is paid $10 if he gets all heads or all tails when 3 coins are tossed, and he pays out $2 if either 1 or 2 heads show. What is his expected gain? What should he pay if either 1 or 2 heads show in order to have a fair game?(3.33)
<9> Let X represent the number that occurs when a fair die is tossed. a) Find the mean of X. (3.5) b) Find the variance of X. (2.917)
<10> On a quiz consisting of five true-false questions, an unprepared student guesses each answer. Find the probability that he gets at least one correct.(31/32)
<11> A box contains 12 transistors, 3 of which are defective. If 3 are sold at random, find the following probabilities. a) None are defective.(21/55). b) exactly 2 are defective.(27/220)
<12> From a box containing 3 white balls and 7 black balls, 8 balls are drawn in succession with replacement. Find the probability distribution for the number of white balls. Find the mean.( (0.7+0.3)^8; 2.4)
<13> The probability that a patient recovers from a heart operation is 0.8. What is the probability that 12 or 13 of the next 15 patients having this operation survive? How many of the 15 patients do you expect to survive? (0.481; 12)
<14> A multiple-choice test has 10 questions, each with 5 possible answers of which only one is the correct answer. What is the probability that sheer guesswork yields from 2 to 5 correct answers? What is the average number of correct answers? (0.617)
<15> A packing company is inspecting a shipment of grapefruit by cutting open 15grapefruit selected at random. The company will accept all grapefruit if 14 or all of these 15 grapefruit are of satisfactory quality. If 95% grapefruit of the shipment are of satisfactory quality, what is the probability that the shipment will be accepted? (0.829)
<16> A box contains 10 $1 bills, 5 $2 bills, 3 $5 bills, 1 $10 bill, and 1 $100. A person is charged $20 to select one bill at random. Find the expectation. Is the game fair? (-12.75)
<17> 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 9? (46/221)
<18> The probability that a student passes history is 0.7, and the probability that he passes chemistry is 0.8 . If the probability of passing at least one course is 0.9, what is the probability that he will pass both courses? (0.6)
<19> A coin is tossed 3 times in succession. What is the probability that one head occurs? (3/8)
<20> In a poker hand consisting of 5 cards, find the probability of holding 2 clubs and 3 diamonds {[C(13,2)*C(13,3)]/C(52,5)}