Discrete Mathematics

Discrete Probability

Probability - Rule of Product

         

There are 66 white beads and 55 black beads in your pocket. You randomly pull the beads one by one out of your pocket and place them on a table. Let ab\frac{a}{b} be the probability that the third bead drawn is the first white bead, where aa and bb are coprime positive integers. What is the value of a+b?a+b?

Two independent, fair 6 sided dice are rolled. The first die face shows a 66. The second die rolls under the table, so you can not see its face. The probability that the dice under the table is 66 given that the first dice is 66 can be written as ab\frac{a}{b}, where aa and bb are positive coprime integers. What is the value of a+ba + b?

Liam has 4 black shirts and 6 white shirts in his closet. He also has 5 black ties and 3 white ties in his drawer. If Liam reaches into the closet and takes out a shirt at random, then reaches into the drawer and takes out a tie at random, then the probability that the shirt and the tie are the same color is ab\frac{a}{b}, where aa and bb are coprime positive integers. What is the value of a+ba+b?

A bag contains 33 red marbles, 44 blue marbles, 66 yellow marbles, and 66 green marbles. Four marbles are randomly drawn from the bag, without replacement. The probability of drawing a red, then blue, then green, and finally another red marble is ab\frac{a}{b}, where aa and bb are positive coprime integers. What is the value of a+ba+b?

The probability that it will rain on any given day in August in Los Angeles is 9%. What is the probability that it rains on both August 13, 2021 and August 13, 2022?

Submit your answer as a decimal.

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