A deck of Uno cards has 4 colors (suits): Red, Yellow, Green, Blue
Each color has cards numbered 1 to 9,
so the total number of these cards = 4*9 = 36
(An Uno deck also has other, special cards, but for this question, those special cards are removed for the deck. Only the numbered cards are used.)

a) Event E = Randomly selecting an UNO card that is Red.
What is the probability of event E?
(Enter a fraction; it does not have to be reduced.)

b) Event F = Randomly selecting an Uno card that is some number from 1 to 6 of any of the 4 colors.
What is the probability of event F?
(Enter a fraction; it does not have to be reduced.)

c) How many cards are in the intersection of events E and F?

d) P(E and F) = the probability of choosing a card in the intersection of events E and F: P(E and F) = ?

e) Let event G = E or F.Use the General Addition Rule to compute P(G): P(G) = P(E) + P(F) - P(E and F)

f) How many cards are in event G?

The appropriate answer of each of the parts is "[tex]\frac{1}{4}[/tex]", "[tex]\frac{4}{9}[/tex]", "[tex]4 \ cards[/tex]", "[tex]\frac{1}{9}[/tex]", "[tex]\frac{21}{36}[/tex]" and "[tex]21 \ cards[/tex]". A complete solution is provided below.

Given:

4 colors = Red, Yellow, Green, Blue

Numbered from 1 to 9

Total number of cards = [tex]4\times 9[/tex]

= [tex]36[/tex]

(a)

The probability of even E will be:

→ [tex]P(E) = \frac{No. \ of \ favorable \ outcomes}{Total \ no. \ of \ outcomes}[/tex]

[tex]=\frac{9}{36}[/tex]

[tex]=\frac{1}{4}[/tex]

(b)

Cards between 1 to 4 = [tex]4\times 4[/tex]

= [tex]16[/tex]

→ [tex]P(F) = \frac{16}{36}[/tex]

[tex]=\frac{4}{9}[/tex]

(c)

There are 1 red, 2 red, 3 red, 4 red, So that the cards satisfy both E and F are:

→ Intersection = [tex]4 \ cards[/tex]

(d)

→ [tex]P(E \ and \ F) = \frac{4}{36}[/tex]

[tex]= \frac{1}{9}[/tex]

(e)

The probability of event G will be:

→ [tex]G = P(E \ or \ F)[/tex]

[tex]= P(E)+P(F) - P(E \ and \ F)[/tex]

[tex]=\frac{1}{4}+\frac{4}{9} -\frac{1}{9}[/tex]

[tex]=\frac{9+16-4}{36}[/tex]

[tex]=\frac{21}{36}[/tex]

(f)

→ Number of cards in the event G will be:

= [tex]9 \ red+4 \ green +4 \ yellow+4 \ blue[/tex]

= [tex]21 \ cards[/tex]

Thus the above answers are correct.

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