Question

homework 5 - conditional probability: problem 7 (3 points) results for this submission 1 of the answers are not correct. 0 of the questions remain unanswered. a deck consists of 60 cards with 3 suits labeled a, b, and c, and numbered ranks from 1 to 20. that is, there are 20 cards of each suit and 3 cards of each rank. a single card is drawn at random from this deck. a) what is the probability of it being suit b? b) what is the probability of it having rank 11? c) what is the probability of it having rank 11 given that it is suit b? hint: among the cards with suit b, how many of them have rank 11? d) what is the probability of it being suit b given that it has rank 11? hint: among the cards with rank 11, how many of them are suit b?

Explanation:

Step1: Calculate total number of cards

The deck has 3 suits with 20 cards in each suit, so the total number of cards $n = 3\times20=60$.

Step2: Calculate probability of suit B

There are 20 cards of suit B. The probability $P(B)=\frac{n(B)}{n}=\frac{20}{60}=\frac{1}{3}$.

Step3: Calculate probability of rank 11

There are 3 cards of rank 11 (one for each suit). The probability $P(11)=\frac{n(11)}{n}=\frac{3}{60}=\frac{1}{20}$.

Step4: Calculate probability of rank 11 given suit B

Among the 20 cards of suit B, there is 1 card of rank 11. So $P(11|B)=\frac{n(11\cap B)}{n(B)}=\frac{1}{20}$.

Step5: Calculate probability of suit B given rank 11

Among the 3 cards of rank 11, there is 1 card of suit B. So $P(B|11)=\frac{n(11\cap B)}{n(11)}=\frac{1}{3}$.

Answer:

a. $\frac{1}{3}$
b. $\frac{1}{20}$
c. $\frac{1}{20}$
d. $\frac{1}{3}$