UNO is a card game. A standard UNO deck consist of 108 cards: four each of Wild and Wild Draw Four, and 25 each of four different colors (red, yellow, green, blue). Each color consists of number cards (one zero, two each of 1 through 9) and two cards each of Skip, Draw Two, and Reverse. These last three types are known as action cards. To begin the game (using a well shuffled deck) a seven card hand is dealt to each player (without replacement). Consider an outcome space without order. Without worrying about how many players are there, find the probability of a player starting of with: a. a whole hand of action cards. b. a hand of cards with out any Wild (Wild or Wild Draw Four) cards. Explain your answer by giving a clear description of an equally-likely outcomes model on which it is based. In other words, tell me what I and events you are using, how many elements they have?

total number of cards = N = 108

wild cards = 4

wild draw four = 4

we have 4 different colors and each color has 25 cards with

break down as

zero numbered card = 1

numbered from 1 to 9 = 2 each (total 18)

skip = 2

draw two = 2

reverse = 2

skip, draw two and reverse are action cards

therefore, in a deck of UNO we have 3*2*4 = 24 action cards

a seven card hand is dealt to each player from a well shuffled

pack of card.

therefore, as each card is equally likely, we have total

possible outcomes as 108C7

where ‘C’ function is a Combination function and it is defined

as

Ω is a event of every possible outcome and it has 108C7

= 27883218168 elements

an equally likely model is a model where equal weights are

attached to every outcome and thus the probability of each outcomes

become equal.

1) let ‘A’ be the event a whole hand is of action

cards.

we have a total of 24 action cards in a UNO deck of 108

cards.and we have to draw a hand of 7 cards

total number of outcomes for event ‘A’ is

24C7

therefore, probability that a player starting with a whole hand

of action cards is

=

= 0.0000124

therefore, a person starts with a whole hand of action

card is 0.0000124

and number of outcomes of event ‘A’ is

346104

2) let ‘B’ be the event that a hand of card is without

any wild card

therefore we have a total of 100 cards that do not have any wild

( wild or wild draw four) cards

therefore a hand of 7 out of 100 cards for event ‘B’ can be

drawn in 100C7 total ways

therefore, the probability that a player starting with a hand of

cards without any Wild (Wild or Wild draw four) cards is

=

= 0.5741

therefore, a person starts with a hand

of cards without any Wild (Wild or Wild draw four) is

0.5741

and number of outcomes of event ‘B’ is

16007560800.

n n! r!(n-r)! r

24C7 108C7

100C7 108C7

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