Question

A fair die is rolled. Find the probability of rolling

a. a 4

b. a 5

c. a number less than 5

d. a number greater than 4

e. a number less than 20

f. a number greater than 17

g. an odd number

h. a 4 or a 5

i. a 4 or an even number

j. a 4 and a 5

k. a 4 and an even number

l. a 4 or an odd

Answer 1

Here for a fair die

P(for any roll from 1 to 6) = 1/6

(a) P(a 4) = 1/6

(b) P(a 5) = 1/6

(c) a number less than 5 = P(x < 5) = P(1) + P(2) + P(3) + P(4) = 4/6 = 2/3

(d) P(x > 4) = P(5) + P(6) = 1/6 + 1/6 = 2/6 = 1/3

(e) P(x< 20) = P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 6/6 = 1

(f)  a number greater than 17

P(x > 17) = 0

g. an odd number

P(an odd number) = P(1) + P(3) + P(5) = 1/6 + 1/6 + 1/6 = 1/2

h. a 4 or a 5

P(a 4 or a 5) = 1/6 + 1/6 = 2/6 = 1/3

i. a 4 or an even number

P(a 4 or an even number) = P(2) + P(4) + P(6) = 3/6 = 1/2

j. a 4 and a 5

P(a 4 and a 5) = P(4) + P(5) = 2/6 = 1/3

k. a 4 and an even number

P(a 4 and an even number) = P(4) = 1/6

l. a 4 or an odd = P(1) + P(3) + P(4) + P(5) = 4/6 = 2/3