1. Three cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is a 4, the second card is a club,and the third card is a 2?
2.In the game Yahtzee, a player rolls five fair dice and gets a Yahtzee if all five dice show the same number. After the initial roll, the player gets two chances to reroll some of the dice. What is the probability that, on the initial roll, at least two of the dice show the same number? Express your answer as a common fraction.
3.In how many ways can 8 people be seated in a row of chairs if three of the people, John, Wilma and Paul, refuse to sit in three consecutive seats?
1) I don't really know much about "playing cards", but isn't it a simple matter of counting?
There are four "4s" in a deck of 52 cards, isn't that right? So, the probability is:
4/52. But the first 4 could a 4 of club(whatever that means!!), so you have only 12 cards of club left.
So, the probability of any of the 12 cards out of 51 remaining cards would be:
12/51. But this 2nd draw could be a 2 of club, so would have left three "2s" out of the remaining 50 cards, 3/50. So, the overall probability would be(if I understand) "playing cards" :
4/52 x 12/51 x 3/50 =144/132,600 =6 / 5,525
Note: Somebody who understands this much better than I should check this out!.
2) The probability of rolling ANY number on 1 die is 1/6. But, you have 5 dice, so the probability of rolling any particular number would be: 5 x 1/6 =5/6. And the probability of rolling the same number again would still be: 5 x 1/6 =5/6. The remaining 3 dice could any number or 6//6 x 6/6 x 6/6. So, the probability of getting two of a kind would be:5^2 x 6^3 / 6^5 =25 / 36
Note: Somebody should check this one as well!.
3) Melody is pretty good at these seating arrangements, so she should take a look at this one!