use the card deck below to answer the questions.\nfor the next few questions, consider the following deck of…

use the card deck below to answer the questions.\nfor 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.\n9 numeric 1 point\nif 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.\nanswer\n10 numeric 1 point\nif 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.\nanswer

use the card deck below to answer the questions.\nfor 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.\n9 numeric 1 point\nif 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.\nanswer\n10 numeric 1 point\nif 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.\nanswer

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