Question

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 3 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?

Explanation:

Part (a)

Step1: Determine total number of cards

The total number of numbered Uno cards is given as \( 4 \times 9 = 36 \).

Step2: Determine number of red cards

Each color (including red) has 9 numbered cards. So, the number of red cards is 9.

Step3: Calculate probability of event E

The probability of an event \( E \) is given by \( P(E)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \). For event \( E \) (selecting a red card), the number of favorable outcomes is 9 (red cards) and total outcomes is 36. So, \( P(E)=\frac{9}{36} \).

Step1: Determine total number of cards

Total numbered Uno cards = 36 (as calculated earlier).

Step2: Determine number of favorable cards for event F

Event F is selecting a card with number 1 - 3 of any of the 4 colors. For each color, there are 3 numbers (1, 2, 3), and there are 4 colors. So, number of favorable cards \( = 4\times3=12 \).

Step3: Calculate probability of event F

Using the probability formula \( P(F)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \), we substitute the values. So, \( P(F)=\frac{12}{36} \).

Step1: Understand intersection of E and F

The intersection of events \( E \) (red cards) and \( F \) (cards with numbers 1 - 3) is the set of red cards with numbers 1 - 3.

Step2: Calculate number of cards in \( E \cap F \)

For red color, the numbers 1 - 3 give 3 cards. So, the number of cards in the intersection is 3.

Answer:

\(\frac{9}{36}\)

Part (b)