Question

Suppose that 4 out of the 17 doctors in a small hospital are general practitioners. 7 out of the 17 are under the age of 45 and 2 are both general practitioners and under the age of 45. What is the probability that you are randomly assigned a general practitioner or doctor under the age of 45? Enter a fraction or round your answer to four decimal places if necessary

Answer 1

Step-by-step explanation:

The probability of general practitioners will be given below as

`Pr(G)=(4)/(17)`

The probability of people under the age of 45 is given below as

`Pr(U)=(7)/(17)`

The probability of people that are both general practitioners and under the age of 45 is given below as

`Pr(G\cap U)=(2)/(17)`

Hence,

To calculate the probability that you are randomly assigned a general practitioner or doctor under the age of 45, we will use the formula below

`Pr(G\cup C)=Pr(G)+Pr(U)-Pr(G\cap C)`

By substituting the values, we will have

Hence,

The final answer is

`\Rightarrow(9)/(17)`