Question

There are twelve shirts in your closet, five blue and seven green. Four of the blue shirts and one of the green shirts fit well. The others are too big. You randomly select a shirt to wear. It is blue or is too big. Find the probability of this occuring

Answer 1

• P (blue or too big) = 11 / 12

Step-by-step explanation:

A two way table permits to represent the situation clearly and find the answser is an easy way.

The two way table is that results from the given information is:

Initial information:

Blue Green Total

Fit well 4 1 ?

Too big ? ? ?

Total 5 7 12

Now by subtraction and addition you can fill the unknown fields:

Blue Green Total

Fit well 4 1 5

Too big 1 6 7

Total 5 7 12

Now, you can see that there are 5 blue and 7 too big shirts, but the total number of them is 5 + 7 - 1 (because one of the too big shirts is also blue).

Then, the number of shirts being blue or too big is 5 + 7 - 1 = 11.

And the probability is :

• P(blue or too big) = number of blue or too big / total number of shirts

• P (blue or too big) = 11 / 12 ← answer

You can also realize that there is only 1 green shirt that fits well, and that is the only option of not being blue of too big, so 1 /12 is the probability of not being blue or too big, and its complement (being blue or too big) is 1 - 1/12 = 11 / 12.