A class quiz has 5 True/False questions. The correct answers are T, T, E, F, and T, in that order. John answered the questions randomly and is now wondering if he will pass the quiz. He needs to have at least 3 correct answers. John
used a calculator to generate random numbers from 1 to 100. He let odd numbers stand for True and even numbers
stand for False. He recorded the results in the table. What is the experimental probability that John passed the quiz?
Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Trial 6 Trial 7 Trial 8
Random 22, 33, 11, 3, 72, 28, 36, 43, 27, 56, 41, 12, 34, 20, 11, 7,50, 17, 44, 76,2, 93, 53,
Numbers 18, 45, 80 98,67
85, 71 90, 55 59, 31 28,82 39,20 38, 29
Result Fail Pass Fail Pass Fail Pass Fail Pass
Experimental nrnhahility

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.