6. A 7-sided die is rolled. Find the probability that the roll results in an odd

Question

6. A 7-sided die is rolled. Find the probability that the roll results in an odd number or a number less than 5 You are shopping at Walmart and your roommate asks you to pick up toothpaste and mouthwash. Your roommate did not mention which brand that they want. Walmart has eight brands of toothpaste and five brands of mouthwash. a. What is the probability that you will buy the correct brands for both items? 7. b. Is this an unusual event? Explain. 8. Find the probability of selecting an ace from a standard deck of 52 playing cards. 9. What is the difference between independent and dependent? Give an example of each. 10. What is the difference between mutually exclusive and not mutually exclusive? Give an example of each 11. When you use the fundamental counting principle, what are you counting? 12. Identify the sample space. Use a tree diagram if necessary. a. Tossing three coins

Explanation / Answer

Answers to the questions till 10.

6. A face in 7 sided die has 1/7 probability of showing up.

1,3,5,7 are odd faces

So, P( odd or a number less than 5)
= {1,2,3,4,5,7}/ {1 to 7}
= 6/7

7. Walmart has 8 brands of toothpaste and 5 brands of mwash

So, a. P(you pick up correct of both items) = 1*1/8C1*5C1 = 1/40

b. It is an usuusal event as the probability of such an event to happen is just 1/40 or .025, which is very less( lesser than critical cutoff of .05)

8. P( ace from deck ) = {4 aces}/52 cards = 4/52 = 1/13

9. Dependent is when Event A' prbobBILITY is dependent on or changes with event B.

Eg. Probability of getting an ace is dependent on getting a spade first. If spade ace comes up first, then probability of getting ace changes

Independent events don't 'interact' with each other. In other words, the 2 events A and B don't affect each other. For example, rolling a die to get 6 and tossing a coin to get a Head are independent of each other.

10. Mutually exclusive events don't have common events between them. Exactly opposite is not mutually exclusive events. Eg. Dogs and Cats are mutually exclusive groups. But if you have 2 groups - boys and girls and want to see a group who has MBA then either boys or girls can have a MBA degree. which means that Boys and Girls having MBA is not mutually exclusive.

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