Question

please enter your answers as fractions.
not every game uses a standard deck of 52 cards with the usual suits and ranks. suppose instead that a certain game uses a deck consisting of 30 cards. the deck has 5 suits labelled a to e, and 6 ranks numbered from 1 to 6. so for example, the deck contains the cards a1, a2, ..., all the way up to a6. there are 6 cards in each suit, and 5 cards in each rank.
suits a to c are red.
suits d to e are blue.
a card is drawn at random from this deck.
a) what is the probability of it being suit a?
b) what is the probability of it having rank 2?
c) what is the probability of it being suit c?
d) what is the probability of it having rank 3?

Explanation:

Step1: Recall probability formula

The probability formula is $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. The total number of cards in the deck is $n = 30$.

Step2: Calculate probability for suit A

Each suit has 6 cards. For suit A, the number of favorable outcomes is 6. So $P(A)=\frac{6}{30}=\frac{1}{5}$.

Step3: Calculate probability for rank 2

Each rank has 5 cards. For rank 2, the number of favorable outcomes is 5. So $P(\text{rank }2)=\frac{5}{30}=\frac{1}{6}$.

Step4: Calculate probability for suit C

Each suit has 6 cards. For suit C, the number of favorable outcomes is 6. So $P(C)=\frac{6}{30}=\frac{1}{5}$.

Step5: Calculate probability for rank 3

Each rank has 5 cards. For rank 3, the number of favorable outcomes is 5. So $P(\text{rank }3)=\frac{5}{30}=\frac{1}{6}$.

Answer:

a) $\frac{1}{5}$
b) $\frac{1}{6}$
c) $\frac{1}{5}$
d) $\frac{1}{6}$