Probability

Mr Pandazis Practice Questions for Test #1 Math 241 1. Define a sample space S for the following experiment. Toss a coin three times and record the outcome for each toss. 2. A card is drawn at random from a standard deck of 52 playing cards so that each card has an equal probability of being drawn. Find the probability of drawing: (a) a card that is neither a club nor a seven; (b) a Jack, Queen, or King; (c) a black card; (d) a red Jack. 3. In selecting 10 cards at random from a deck of 52 cards, what is the probability of selecting 3 clubs, 2 hearts, 4 spades, and one diamond? 4. Count the distinct permutations of all the letters in the word mathematics. 5. In how many ways can there be a first place, second place, and third place winner in a race with 20 runners? Note that there are no ties. 6. A box contains 20 red, 15 white, and 5 blue balls. A ball is chosen at random from the box. If the ball chosen is not white, what is the probability it is not red? 7. Let A, B, and C be events with P(A) = .6, P(B) =.3, P(C) = .4, P(AB) = .2, P(BC) = 0, P(AC) = .1. Find: (a) P(AB'C') (c) P(C'B|C') (b) P(A|B) (d) P(B'|(AUC)