Question

A ball is chosen at random from a bag containing 150 balls that are either red or blue and either dull or shiny. There are 36 red shiny balls and 54 blue balls. What is the probability of the chosen ball being shiny conditional on it being red

Answer 1

The probability of the chosen ball being shiny conditional on it being red is 1.

Step-by-step explanation:

To find the probability of the chosen ball being shiny conditional on it being red, we can use the formula for conditional probability: P(shiny | red) = P(shiny and red) / P(red)

In this case, the number of red shiny balls is 36 and the total number of balls is 150. So, P(shiny and red) = 36/150. The number of red balls is 36 and the total number of balls is 150, so P(red) = 36/150.

Therefore, P(shiny | red) = (36/150) / (36/150) = 1.

Answer 2

The probability of the chosen ball being shiny conditional on it being red is; 0.375

Step-by-step explanation:

Let A be the event that a red ball has been chosen

Let B be the event that a shiny ball has been chosen

Let S be the total outcomes = 150 balls

Thus;

P(A ∩ B ) = 36/150

A ∩ B' = 150 - 36 - 54

A ∩ B' = 60

Thus; P(A ∩ B') = 60/150

P(A') = 54/150

P(A) = (150 - 54)/150 = 96/150

Thus, probability of the chosen ball being shiny conditional on it being red is;

P(B | A) = P(B ∩ A)/P(A)

Thus; P(B | A) = (36/150)/(96/150)

P(B | A) = 0.375