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Homework: The Multiplication Rule

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides practice problems which develop concepts related to the multiplication rule in probability.

Exercise 1

Eli and Beth each chooses a letter of the alphabet, completely at random.

  • a. What is the probability that Eli and Beth both choose the letter “A”?
  • b. What is the probability that Eli and Beth both choose vowels?
  • c. What is the probability that Eli chooses a letter that appears somewhere in the word “Eli,” and Beth chooses a letter that appears somewhere in the word “Beth”?

Exercise 2

In your hand, you hold two regular 6-sided dice. One is red, and one is blue. You throw them both.

  • a. If both dice roll “1” that is sometimes referred to as “snake eyes.” What is the probability of snake eyes?
  • b. What is the probability that both dice will roll even numbers?
  • c. What is the probability that both dice will roll the same as each other?

Exercise 3

A deck of cards contains 52 different cards, assuming there are no jokers. On the table in front of you sit 5 different decks of cards. All of them have been shuffled, so the cards in each deck are in random order.

  • a. What is the probability that the top card in the first deck is the ace of spades?
  • b. What is the probability that the top card in the second deck is the ace of spades?
  • c. What is the probability that the top card in the first two decks are both the ace of spades?
  • d. What is the probability that the top card in all five decks are the ace of spades?

Exercise 4

According to http://www.m-ms.com/, a bag of Milk Chocolate (plain) M&Ms® contains 13% brown, 14% yellow, 13% red, 24% blue, 20% orange, and 16% green M&Ms. A bag of Peanut M&Ms® contains 12% brown, 15% yellow, 12% red, 23% blue, 23% orange, and 15% green.

  • a. If you choose one M&M at random from a Milk Chocolate bag, what is the probability that it will be brown?
  • b. If you choose one M&M at random from a Milk Chocolate bag, what is the probability that it will be brown or yellow?
  • c. If you choose one M&M at random from a Peanut bag, what is the probability that it will be brown or yellow?
  • d. If you choose one M&M at random from a Milk Chocolate bag, and one M&M at random from a Peanut bag, what is the probability that they will both be brown or yellow?

Exercise 5

What is the probability that a married couple were both born...

  • a. In the first half of the year?
  • b. In January?
  • c. On January 1?

Exercise 6

The probability that a given event will occur has been calculated as exactly 5/13. What is the probability that this event will not happen?

Note:

Hint: Start by thinking about easier numbers, such as 1 2 1 2 or 1 4 1 4 .

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