Ex General Probability 2

# Ex General Probability 2 - your answers change Why or why...

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Examples 9-10-08 1. Suppose a fair twenty-sided die is rolled 6 times. Let A be the event that at least one 7 is rolled. a. How many possible outcomes are there? b. Define A C in words. c. Find P(A). d. If we allow n to vary, how large must n be in order for P(A)> .95? 2. Suppose a fair ten-sided die is rolled 11 times. Let B be the event that at least one “big number” is rolled. We define a big number as 9 or 10. a. How many possible outcomes are there? b. Find P(B). c. If we allow n to vary, how large must n be in order for P(B)>.99? 3. Suppose a box contains 2 blue balls, 8 red balls, and 40 black balls. Let us sample n balls with replacement and record the color of the ball drawn. Let P(R) denote the probability of getting at least one red ball in the sample of n balls. a. How many possible outcomes are there if n=7? b. Find P(R) if n=7. c. Find P(R) if we do not specify n. d. Using your answer to c, how large must n be for P(R) to be larger than .997? e. If we labeled the balls with numbers from 1 to 50, repeat part a and b. Do
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Unformatted text preview: your answers change? Why or why not? 4. Suppose a particular website makes you have a password of 6 characters. Your characters can be a lower-case letter or a number. a. How many possible outcomes are there? b. If you choose a password at random (no restrictions on the password), what is the probability that it contains at least one 5? c. If you can also use capital letters, how many possible outcomes are there? 5. Suppose a lock has a number dial from 1 to 75 and your code must have only 3 digits. a. How many possible codes are there? b. If you cannot have the same number next to each other, how many codes are there? c. If you cannot repeat a number anywhere in the code, how many codes are there? d. Define PR to be the set {2,3,5,7,9} i.e. the prime numbers smaller than 10. What is the probability of at least one member of PR being selected if you choose a code at random?...
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