Solution please

3. There are 13 standard decks of cards. Each deck is shuffled, separately. The 13 decks are lined up in a row on the table. The top card is drawn from each deck. What is the probability that at least 3 cards of each suit are drawn?

Solution please

4. A hand of 5 cards contains 2 red cards and 3 black cards. Trish plays the following game: A card is drawn from the hand. If the card is red, the game stops immediately. If the card is black, this black card is set aside and a red card is put into the hand in its place. Then another card is drawn from the hand and the same process is repeated. The game continues until Trish draws a red card ( Note that there are always 5 cards in the hand before Trish draws a card.) Let X be the number of black cards Trish drew during the game. (That is, the value of X is determined after the game has finished.) (a) Make a table showing the probability distribution function(pdf) and cumulative distribu... click for more

Soluton please

5. Let E be the event that the number which comes up when a single die is tossed is divisible by 3. Let X be the number of times that event E occurs in 3 tosses of the die. (a) Make a table showing the pdf and the cdf of X. (b) Find E(X) and V(X).

Solution please

6. Use the Binomial tables to find the following values: (a) Pr[B(10, .3)>4] (b) Pr[3≤B(7, .2) (less than) 6] (c) Pr[B(12, .6) ≥7]

Solution please

7. There are some tokens in a bag. Each token has a number ( a positive integer) printed on it. Ernesto does not know how many tokens are in the bag, and the only thing he knows about the numbers on them is that the mean of the numbers is 3 and the variance is 2. Ernesto is going to play a game in which he draws 1 token from the bag and is paid an amount in dollars equal to the square of the number printed on the token that he draws. For instance, if he draws a 2 he will receive $4, but if he draws a 5 he will receive $25. What is the maximum that Ernesto should be willing to pay to play this game if he wants to be sure that on average, if he plays very many times, he shouldn't lose money?... click for more