Question

Rob determined that some teenagers like to eat hot dogs, some like to eat hamburgers, and others don't like to eat hotdogs or hamburgers. He calculated the probabilities and created the Venn diagram below:
a venn diagram showing two categories, Hot dogs and Hamburgers. In the hot dogs only circle is 0.3, in the hamburger only circle is 0.4, in the intersection is 0.1, outside the circles is 0.2

What is the probability that a teenager eats hotdogs, given that he/she eats hamburger

Answer 1

Answer: 0.2

Step-by-step explanation:

Given: According to the Venn diagram,

The probability that a teenager eats hamburger and hot dogs P(H∩D)=0.1

The probability that a teenager eats hamburger P(H)= Teenager eats hamburger only + intersection =0.4+0.1=0.5

Now,  the probability that a teenager eats hotdogs, given that he/she eats hamburger is given by :-

$P(D|H)=\frac{P(H∩D)}{P(H)}\\\\=\frac{0.1}{0.5}=0.2$

Hence, the  probability that a teenager eats hotdogs, given that he/she eats hamburger= 0.2

Answer 2

.5
.4 + .1 = .5
......