SCAVONE A fair 20-sided die is rolled. (This die has 20 faces, numbered 1-20.) F

Question

SCAVONE A fair 20-sided die is rolled. (This die has 20 faces, numbered 1-20.) Find the probabilities of the following results. Use the correct svmbol for the probability and write probabilities as reduced fractions. Show your work! a. Event E, which is rolling a number divisible by 11 4. b. Event F, which is rolling a number divisible by 10. c. Event G, which is rolling a number divisible by 4. d. Event E or F. e. Event F and G f. Event For G g. Event F, given that we know event G has occurred.

Explanation / Answer

Possible outcomes = { 1 2 3 4 5 ...........20}

Total no. of outcomes = 20

a) E (divisible by 11)

{11} - 1 element

P(E) = 1/20 = 0.05

b) F (divisible by 10)

{10,20} - 2 elements

P(F) = 2/20 = 0.10

c) G (divisible by 4)

{4 8 12 16 20} - 5 elements

P(G) = 5/20 = 0.25

d) E or F

P(E or F ) = P(E) + P(F) - P(E).P(F)

= 0.05 + 0.10 - (0.05)(.10)

= 0.145

e)
P(F and G) = P(F)*P(G)

= .10 * .25

= 0.025

f)

P(F or G) = P(F)+P(G) - P(F)*P(G)

= 0.25 +.10 -0.025

= 0.325

g) P(F | G ) = P(F and G) / P(G)

= 0.025 / 0.25 = 0.10

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