Question

Karl has 5 blue pencils, 3 yellow pencils and 2 black pencils. If Karl selects 2 pencils at random from his pencil case, without replacement, what is the probability that both pencils are not yellow?

Answer 1

The probability is 42/90 simplified to 7/15

Equation: probability of first non-yellow pencil x probability of second non-yellow pencil
7/10*6/9= 42/90= 7/15

There are 7 total pencils that are not yellow but because you don’t put the non-yellow pencil back there is a decrease in both the non-yellows and total pencils!

Answer 2

In total you have 10 pencils but only 2 of them are yellow. Therefore when simplify this, the changes of not picking a yellow pencil is 8/10 which simplify to 4/5. There’s a 4/5 chance neither pencils will be yellow