How many passwords are possible if digits may not be repeated? There are five tiles in a bag, labeled W, O, R, D, and S. A tile is chosen at random and then another tile is chosen at random. Determine whether the following events are independent or dependent. (Ex4) Choose W and then choose S , if the first tile is replaced before the f. Second tile is chosen. g. Choose W and then choose S , if the first tile is not replaced before the second tile is chosen. h. There are 9 players in a starting baseball lineup. How many ways can batting positions 1,2 , and 3 be filled, choosing from 9 players?

A card is drawn randomly from a standard 52 -card deck. Find the probability of the given event. (a) The card drawn is 5 The probability is : (b) The card drawn is a face card (Jack, Queen, or King) The probability is: (c) The card drawn is not a face card.

If \( f(x)=k(1-x) \quad 0<x+1 \) Find \( P(x>0.25) \)

A jar contains 6 red marbles numbered 1 to 6 and 8 blue marbles numbered 1 to 8 . A marble is drawn at random from the jar. Find the probability of the given event. (a) The marble is red Your answer is: (b) The marble is odd-numbered Your answer is: (c) The marble is red or odd-numbered Your answer is: (d) The marble is blue and even-numbered Your answer is:

Tickets for a raffle cost \( \$ 11 \). There were 730 tickets sold. One ticket will be randomly selected as the winner, and that person wins \( \$ 1400 \) and also the person is given back the cost of the ticket. For someone who buys a ticket, what is the Expected Value (the mean of the distribution)? If the Expected Value is negative, be sure to include the "-" sign with the answer. Express the answer rounded to two decimal places. Expected Value \( =\$ \$ \)

Round your answer to 4 decimal places, if necessary. What is the probability of pulling out: a) a face card? \( P( \) face \( )= \) b) a diamond or a spade? \( P \) (diamond or spade) \( =\square \) c) a 3 or a 9 ? \( P(3 \) or 9\( )= \) d) an ace or a heart? \( P( \) ace or heart \( )=\square \) e) a face card or a spade? \( P( \) face or spade \( )= \) f) a 7 or a red card? \( P(7 \) or red \( )=\square \)