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

Given:
Probability of eating hot dogs only - 0.30
Probability of eating hamburgers only - 0.40
Probability of eating both - 0.1
Probability of not eating any of the 2 - 0.20

Probability of eating hot dogs, given that he/she eats hamburgers

P (Hd | Hb) = P (Hd and Hb) / P(Hb) = 0.10 / 0.40 = 0.25

The probability that a teenager eats hot dogs, given that he/she eats hamburgers is 0.25 or 25%.

Answer 2

0.25

Explanation:

We are given that Rob created the Venn Diagram shown below which gives us,

The probability of teenagers who like to eat hot dogs = P(HD) = 0.3

The probability of teenagers who like to eat hamburger = P(HB) 0.4

The probability of teenagers who like to eat both = P( HD ∩ HB ) =0.1

The probability of teenagers who like to eat none = 0.2

It is required to find the probability that a teenager eats hot dogs when it is given that he/she eats hamburger i.e. P( HD | HB ).

Now, we know that the probability that an event B occurs given that event A has already occurred is given by,

`P(B|A) = (P(A \bigcap B))/(P(B))`

So,
`P(HD|HB) = (P(HD \bigcap HB))/(P(HB))`

i.e.
`P(HD|HB) = (0.1)/(0.4)`

i.e.
`P(HD|HB) = 0.25`

Hence, the probability that a teenager eats hot dogs when it is given that he/she eats hamburger is 0.25.