The probability of two in a row

Difficulty Stretch · Set kzbd69

Give each probability as a fraction in its lowest terms.

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1
A bag holds 2 yellow counters and 12 red ones. One is taken, put back, and another is taken. What is the probability that both are yellow?
2
A bag holds 8 red counters and 9 green ones. One is taken, put back, and another is taken. What is the probability that both are red?
3
A bag holds 2 black counters and 12 green ones. One is taken, put back, and another is taken. What is the probability that both are black?
4
A bag holds 6 yellow counters and 11 red ones. One is taken, put back, and another is taken. What is the probability that both are yellow?
5
A bag holds 2 blue counters and 1 yellow one. One is taken, put back, and another is taken. What is the probability that both are blue?
6
A bag holds 4 green counters and 8 black ones. One is taken, put back, and another is taken. What is the probability that both are green?
7
A bag holds 6 green counters and 6 red ones. One is taken, put back, and another is taken. What is the probability that both are green?
8
A bag holds 9 green counters and 2 blue ones. One is taken, put back, and another is taken. What is the probability that both are green?
9
A bag holds 9 yellow counters and 10 red ones. One is taken, put back, and another is taken. What is the probability that both are yellow?
10
A bag holds 1 black counter and 10 green ones. One is taken, put back, and another is taken. What is the probability that both are black?
11
A bag holds 1 green counter and 4 blue ones. One is taken, put back, and another is taken. What is the probability that both are green?
12
A bag holds 3 black counters and 9 red ones. One is taken, put back, and another is taken. What is the probability that both are black?
13
A bag holds 1 black counter and 8 red ones. One is taken, put back, and another is taken. What is the probability that both are black?
14
A bag holds 8 black counters and 7 blue ones. One is taken, put back, and another is taken. What is the probability that both are black?
15
A bag holds 5 green counters and 3 yellow ones. One is taken, put back, and another is taken. What is the probability that both are green?
16
A bag holds 10 blue counters and 5 red ones. One is taken, put back, and another is taken. What is the probability that both are blue?
17
A bag holds 6 black counters and 5 green ones. One is taken, put back, and another is taken. What is the probability that both are black?
18
A bag holds 11 green counters and 3 red ones. One is taken, put back, and another is taken. What is the probability that both are green?
19
A bag holds 1 black counter and 11 red ones. One is taken, put back, and another is taken. What is the probability that both are black?
20
A bag holds 7 yellow counters and 12 green ones. One is taken, put back, and another is taken. What is the probability that both are yellow?

What is in this set

The numbers in this set run from 1 to 12.
Every problem in it will ask for two draws in a row.
A careful solution takes 3 written steps on average.
The mistake this set invites most often, in 100% of the problems: the two probabilities were added; for one outcome and then another, they are multiplied.
Answers are a fraction in its lowest terms, written like 3/4.

Drawing 240 problems from this page produced 232 different ones, 97% — so a sheet of 20 is a new sheet almost every time.

The same skill, harder or easier

We would put this in front of a grade 8 class. That is our judgement, not a standard, and it is printed here so you can disagree with it. Everything else we put in that year.