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 4 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)

Explanation:

Part a) Step1: Identify total and favorable outcomes

Total cards (numbered) = 36. Red cards: each color has 9, so red has 9.

Part a) Step2: Calculate probability

Probability \( P(E) = \frac{\text{Number of red cards}}{\text{Total numbered cards}} = \frac{9}{36} \)

Part b) Step1: Find number of favorable cards for F

Numbers 1 - 4, 4 colors. So per color: 4 cards, 4 colors: \( 4 \times 4 = 16 \)

Part b) Step2: Calculate probability for F

\( P(F) = \frac{\text{Number of cards for F}}{\text{Total numbered cards}} = \frac{16}{36} \)

Part c) Step1: Determine intersection (E and F)

E: red cards; F: numbers 1 - 4. So red cards with numbers 1 - 4: 4 cards (1 - 4, red).

Part c) Step2: Count the intersection

Number of cards in \( E \cap F \) is 4.

Part d) Step1: Use intersection count for probability

Total cards = 36, intersection count = 4. So \( P(E \text{ and } F) = \frac{4}{36} \)

Part e) Step1: Substitute values into General Addition Rule

\( P(G) = P(E) + P(F) - P(E \text{ and } F) = \frac{9}{36} + \frac{16}{36} - \frac{4}{36} \)

Part e) Step2: Compute the result

\( \frac{9 + 16 - 4}{36} = \frac{21}{36} \)

Answer:

s:
a) \(\frac{9}{36}\)
b) \(\frac{16}{36}\)
c) \(4\)
d) \(\frac{4}{36}\)
e) \(\frac{21}{36}\)