Question

use the card deck below to answer the questions-
for the next few questions, consider the following deck of 20 cards which have 4 suits labelled x,y,z,w and 5 ranks labelled 1,2,3,4,5. the two suits x,y are colored white and the two suits z,w are colored grey. when drawing cards, each individual card is equally likely.
6 numeric 1 point
if you draw a card randomly from the above deck of cards, what is the probability that it is in suit z? enter your answer as a decimal.
answer
7 numeric 1 point
if you draw a card randomly from the above deck of cards, what is the probability that it is in rank 3 or rank 4? enter your answer as a decimal.
answer
8 numeric 1 point
if you draw a card randomly from the above deck of cards, what is the probability that it is in rank 3 and is gray? enter your answer as a decimal.
answer

Explanation:

Step1: Recall probability formula

Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. The total number of cards is 20.

Step2: Solve for question 6

For the probability of drawing a card of suit Z, the number of cards in suit Z is 5. So the probability $P(Z)=\frac{5}{20}= 0.25$.

Step3: Solve for question 7

The number of cards of rank 3 is 4 and the number of cards of rank 4 is 4. But we need to avoid double - counting. The number of favorable outcomes for rank 3 or rank 4 is $4 + 4=8$. So the probability $P(\text{rank 3 or rank 4})=\frac{8}{20}=0.4$.

Step4: Solve for question 8

The gray - colored suits are Z and W. The cards that are rank 3 and gray are Z3 and W3. So the number of favorable outcomes is 2. The probability $P(\text{rank 3 and gray})=\frac{2}{20}=0.1$.

Answer:

1. 0.25
2. 0.4
3. 0.1