Question

Darren just returned from a spring break volunteer trip. He is shopping for a photo album that will showcase his photos from the trip. The albums range in photo capacity and orientation. Horizontally Vertically 3 5 50 photos 100 photos 150 photos 3 5 3 1 What is the probability that a randomly selected photo album holds exactly 150 photos given that the photo album is oriented horizontally? Simplify any fractions.

Answer 1

You have to determine the probability of the photo album having 150 photos, given that the album is it oriented horizontally, symbolically:

`P(150|horizontal)`

To determine this probability, you can use the definition of conditional probability which states that, given two events A and B, that are not independent, the probability of A given that B has already occurred is equal to the quotient between the probability of the intersection of A and B and the probability of B

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

The first step is to determine the probability of "150 phonos and horizontal", to do so you have to divide the number of albums that had 150 photos and are horizontal by the total number of observations

`P(150\cap horizontal)=(3)/(20)`

The second step is to determine the probability of the albums being horizontal, to do so you have to divide the total number of albums that were horizontal by the total number of albums:

`P(horizontal)=(9)/(20)`

The third step is to calculate the conditional probability:

`\begin{gathered} P(150|\text{horizontal)}=(P(150\cap horizontal))/(P(horizontal)) \\ P(150|\text{horizontal)}=((3)/(20))/((9)/(20)) \\ P(150|horizontal)=(3)/(20)\cdot(20)/(9) \\ P(150|horizontal)=(1)/(3) \end{gathered}`

The probability of the album having 150 photos, given that is oriented horizontally is 1/3