Page E-50
4. Solve.
(N) If you flip a coin 150 times, about how many times would you expect to get heads?
You should get 75 times of getting a head... or 1/2 because there is a 50% of chance that you can get a head and another 50% of getting a tail if you flip the coin once. So flipping the coin 150 times will give you an expectation of 75 because 50% of 150 of 75.
(C) The letters a, e, i, o, u, and y are vowels. If one letter of the alphabet is chosen at random, what is the probability it is a vowel?
The answer should be 6/26 or if you simplify it (by the number 2), you should get 3/13 because the alphabet has 26 letters in total and the vowels would be 6 letters out of 26. Also Mr. Harbeck has taught us an easy way of figuring what the answer would be for questions like this.
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vowels
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total letters of alphabet
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6____ 3
----- = -----
26 ___13
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(K) If you randomly pick a date in April, how many equally likely outcomes are there?
Usually each months should have only 30 or 31 days unless it's February then you have 28 days and if it's a leap year then you get 29 days in February. But we only need to solve for the month of April and the equally likely outcomes should be 30 because April only has 30 days so the number of 30 days is most likely to be the outcomes of April. So if you pick a ramdomly date in April, you should be picking a date between April 1st and April 30th. I have also checked the calendars of the year 2004 and 2005 to make sure that April has only 30 days.
(P) A magician asks you to pick a card, any card, from a standard deck of 52 cards. What is the probability of picking an Ace?
The answer should be a 4 because every number has 4 cards each, a card of hearts, clubs, spades and diamonds. Also, there are 13 numbers (and letters) in a deck. A number 2, 3, 4, 5, 6, 7, 8, 9, and letters such as an Ace, Jack, Queen and a King. So there are 52 cards in a deck, and each number contains 4 cards each, so the probability of getting an Ace is 4/52 or if you simplify it by the number 4, you will get 1/13.
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number of Aces in deck
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number of cards in deck
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4______ 1
------- = -------
26 _____13
My own question:
The prize of $500 dollars is only won by winning the 1st bingo game. The other 5 winners will win $20 dollars. If you were playing bingo with the other 299 people and each person only has 1 bingo card, what is the probability of winning $500 ? What is the probability of winning $20? What is the probability of winning $500 and $20?
P.S. Hints are given =)
K.V. 8-41 (October 16, 2006)
