a box contains 3 black balls , 7 white balls and 5 red balls . one ball is lost . the probability that a red ball is drawn is 2/7 . The colour of the lost ball is
Of the 15 balls, 14 remain.
P(red) = 2/7 means there are 4 red balls out of 14.
So, the lost ball is red.
To determine the color of the lost ball, we can use the concept of conditional probability.
Let's say the color of the lost ball is X. We need to find the probability P(X=red) given that a red ball is drawn with a probability of 2/7.
First, let's calculate the probability of drawing a red ball from the box, denoted as P(Red):
P(Red) = Number of red balls / Total number of balls
= 5 / (3 + 7 + 5)
= 5 / 15
= 1/3
We are given that P(Red) = 2/7. Therefore, we can set up the following equation using conditional probability:
P(X=red | Red) = P(X=red and Red) / P(Red)
We want to find the value of P(X=red and Red), which represents the probability of both the lost ball being red and the drawn ball being red.
Since P(X=red and Red) = P(Red), we can rewrite the equation as:
P(X=red | Red) = P(Red) / P(Red)
= 1/3 / 2/7
= 1/3 * 7/2
= 7/6
Therefore, the probability that the lost ball is red, given that a red ball is drawn, is 7/6 (which is greater than 1). This suggests a mathematical inconsistency, so it seems the provided information is not consistent.