A box has 5 red ribbons and 10 blue ribbons numbered with “1”, 10 red ribbons and 15 blue numbered with 2. What is the probability that one will be chosen will be a red ribbon or numbered “1”?

Answer 1

5 red and 10 blue in one box all numbered 1

10 red and 15 blue in 2nd box all numbered 2

pick one ribbon at random, what is probability it's red or 1??

Pr(1) = 1/2

Pr(r) = 1/2

Pr(1 or r) = 1/2 + (1/2)(10/25) = 1/2 +1/5 = 7/10 = 70% chance

note: Pr(1 or r) is not chance of 1 and r, which is smaller

Pr(1 or r)=9/10 does not equal Pr(1 and r)= 5/40 = 1/8

draw a Venn diagram

or

Pr(1) + Pr(r) - Pr(1^r) = 1/2 + 15/40- 1/6 1/2 +3/8 -1/8 = 7/8-1/8 = 6/8 = 3/4 = 75% chance

ok that gives 2 different answers. at least 1 is wrong. go with 7/10

but 70 and 75% are very close. virtually the same percent in the grand scheme of things

Answer 2

P(red) + P(1) - P(red and 1)