Richard has just been given a 10-question multiple-choice quiz in his history class. Each question has four answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all ten questions, find the indicated probabilities. (Round your answers to three decimal places.)

Step-by-step explanation:

To find the probability that he answered all correctly

let n be the number of questions correctly answered

prob of correct 1/4 = 0.25

prob of answering all correctly:

p(n=10): 0.25∧10 = 0.000000953

prob of wrong  3/4 = 0.75

Prob that he will fail the 10:

prob(n=0): 0.75∧10 =0.0563

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .