What is the probability of spinning less then 4 on a 5 section spinner or rolling a number less then 4 on a 6 sided number cube?

Answer 1

Assuming the spinner has sections numbered 1-5 then:

Pr(Spin < 4) = 3/5 (= 0.6 or 60%)

Pr(Roll > 4) = 3/6 = 1/2 (= 0.5 or 50%)

Assuming both done together:

Pr(spin < 4 or roll < 4)

= Pr(spin < 4) + Pr(roll < 4) - Pr(spin < 4 and roll < 4 [at same time])

= 3/5 + 1/2 - 3/5 × 1/2

= 6/10 + 5/10 - 3/10

= 8/10

= 4/5 (= 0.8 or 80%)

It can also be calculated out by working out the probability of not spinning less than 4 and not rolling less than 4 (at the same time), and then subtracting this from 1 (or 100%):

Pr(spin < 4 or roll < 4)

= 1 - Pr(spin ≥ 4 and roll ≥ 4)

= 1 - (1 - 3/5) x (1 - 1/2)

= 1 - 2/5 x 1/2

= 1 - 1/5

= 4/5 (= 0.8 or 80%)