Question

The game of Fizzbin is played with a deck of 30 cards. There are three colors (red, black, blue), with 10 cards in each color (cards are numbered from 1 to 10). Enter your answers as reduced fractions, with / for the fraction bar and no spaces.

a) If a card is drawn at random, what is the probability that the card is black?

b) If a card is drawn at random, what is the probability that the card is black or has a number less than 5?

c) If a card is drawn at random, what is the probability that the card is a 10?

d) If the first card is a 10, what is the probability that the second card will also be a 10?

e) What is the probability that the first and second cards are both 10s?

Answer 1

a) P(the card is black) = 10/30 = 1/3

b) P(black or less than 5) = 10/30 + 12/30 - 4/30 = 18/30 = 3/5

c) P(the card is a 10) = 3/30 = 1/10

d) P(second card is 10 | first card is 10) = P(first card is 10 and second card is 10)/P(first card is 10)

                                                                 = (3/30 * 2/29)/(3/30) = 2/29

e) P(first and second card are both 10) = 3/30 * 2/29 = 1/145