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.
9 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 is gray? enter your answer as a decimal.
answer
10 numeric 1 point
if you draw a card randomly from the above deck of cards, what is the probability that it is not in rank 3 or gray? this is the complement of the answer you found above (probability of being rank 3 or gray). enter your answer as a decimal.
answer

Explanation:

Step1: Calculate number of cards in rank 3 or gray

There are 4 cards of rank 3 (X3, Y3, Z3, W3) and 10 gray - colored cards (Z1 - Z5, W1 - W5). But Z3 and W3 are counted twice. So the number of cards in rank 3 or gray is $4 + 10-2=12$.

Step2: Calculate probability

The total number of cards is 20. The probability $P$ of drawing a card that is in rank 3 or gray is $P=\frac{12}{20}=0.6$.

Step3: Calculate probability of the complement

The probability of an event $A$ and its complement $\overline{A}$ satisfy $P(A)+P(\overline{A}) = 1$. Since the probability of a card being in rank 3 or gray is 0.6, the probability of a card not being in rank 3 or gray is $1 - 0.6=0.4$.

Answer:

0.4