Question

What is the probability that someone who does not take vitamins is a female? Round to three decimal places.

Female
Male
Total
(1 point)
O 0.374
O 0.139
O 0.080
O 0.626
Takes vitamins
248
145
193
Does not take vitamins
40
67
107
Total
288
212
500

Answer 1

A) 0.374

Explanation:

Let event A be that the person is female.

Let event B be that the person does not take vitamins.

`\boxed{\sf Probability\:of\:an\:event\:occurring = (Number\:of\:ways\:it\:can\:occur)/(Total\:number\:of\:possible\:outcomes)}`

Therefore, from the given table:

`\sf P(A) = (288)/(500)=0.576`

`\sf P(B) = (107)/(500)=0.214`

`\sf P(A \cap B)=(40)/(500)=0.08`

To calculate the probability that someone is female (Event A), given that they do not take vitamins (Event B), use the conditional probability formula for A given B:

`\boxed{\begin{minipage}{5 cm}\underline{Conditional Probability formula}\\\\A given B:\\\\$\sf P(A|B)=(P(A \cap B))/(P(B))$\\\end{minipage}}`

`\sf \implies P(A|B)=(0.08)/(0.214)=0.374\;(3\;s.f.)`