Question

Suppose that 7 out of the 17 doctors in a small hospital are General Practitioners, 4 out of the 17 are under the age of 45, and 2 are both General Practitioners andunder the age of 45. What is the probability that you are randomly assigned a General Practitioner or a doctor under the age of 45? Enter a fraction or round youranswer to 4 decimal places, if necessary.

Answer 1

We need to find the probability that you are randomly assigned a General Practitioner or a doctor under the age of 45.

In order to find this probability, we need to find the number of doctors that are General Practitioner or under under the age of 45. Then, divide that number by he total of 17.

We know that 7 doctors are General Practitioners. And 2 of them are also under the age of 45.

Therefore, since ther are 4 doctors that are under the age of 45, there are 2 additional doctors, besided those 2 that follow in both categories, there are under the age of 45.

Summarizing, the number of doctors that are General Practitioner or a doctor under the age of 45 is:

`7+2=9`

Notice that this result can also be obtained by the formula:

`|A\cup B|=|A|+|B|-|A\cap B|`

where A is the set of General Practitioners, B is the set of doctors under the age of 45, and the symbol |...| represents the number of elements in that set:

`|A\cup B|=7+4-2=9`

Therefore, the required probability is:

Answer

`(9)/(17)`