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) f) how many cards are in event g?

Explanation:

Step1: Calculate probability of event E

The total number of cards is 36. The number of red - numbered cards is 9. So, $P(E)=\frac{\text{Number of red cards}}{\text{Total number of cards}}=\frac{9}{36}$.

Step2: Calculate probability of event F

Each color has 4 cards numbered 1 - 4. So the number of cards in event F is $4\times4 = 16$. Then $P(F)=\frac{\text{Number of 1 - 4 cards}}{\text{Total number of cards}}=\frac{16}{36}$.

Step3: Calculate number of cards in intersection of E and F

The intersection of E (red cards) and F (cards numbered 1 - 4) are the red cards numbered 1 - 4. There are 4 such cards.

Step4: Calculate probability of intersection of E and F

$P(E\cap F)=\frac{\text{Number of red 1 - 4 cards}}{\text{Total number of cards}}=\frac{4}{36}$.

Step5: Calculate probability of event G using addition rule

$P(G)=P(E)+P(F)-P(E\cap F)=\frac{9}{36}+\frac{16}{36}-\frac{4}{36}=\frac{9 + 16-4}{36}=\frac{21}{36}$.

Step6: Calculate number of cards in event G

Since $P(G)=\frac{\text{Number of cards in G}}{\text{Total number of cards}}$ and $P(G)=\frac{21}{36}$, and total number of cards is 36, the number of cards in G is 21.

Answer:

a) $\frac{9}{36}$
b) $\frac{16}{36}$
c) 4
d) $\frac{4}{36}$
e) $\frac{21}{36}$
f) 21