Question

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Mary has 2 bags of tiles. The first bag contains 6 pink tiles, 5 blue tiles, and 4 green tiles. The second bag contains 3 pink tiles, 2 blue tiles and 4 green tiles. Mary will randomly select 1 tile from each bag.



What is the probability that Mary will select a blue tile from each bag?





Explain how you would solve this problem in 5 steps and state your final answer.

Answer 1

The probability that Mary will select a blue tile from each bag is 2/27

Explanation:

Step 1:

Calculate the total number of tiles in 1st bag,

there are, 6 + 5 + 4 = 15 tiles

Step 2:

Calculate the total number of tiles in 2nd bag,

there are 3+2+4 = 9 tiles

Step 3:

Calculate the probability of selecting a blue tile from 1st bag,

since there are 5 blue tiles, we get the probability,

`5/15 = 1/3`

so the probability is 1/3

Step 4:

Calculate the probability of selecting a blue tile from 2nd bag,

since there are 2 blue tiles out of a total of 9,

the probability is 2/9

Step 5:

Multiply both probabilities to find the total probability of getting a blue tile from both

so, (probability of selecting blue tiles from 1st bag)((probability of selecting blue tiles from 2nd bag) = total probability

`(1/3)(2/9) = 2/27`

so the probability that Mary will select a blue tile from each bag is 2/27