Question

In the game of Pick-A-Ball, there are 10 colored balls: 2 red, 4 white, and 4 blue. The balls have been placed into a small bucket, and the bucket has been shaken thoroughly. You will be asked to reach into the bucket without looking and select 2 balls. Because the bucket has been shaken thoroughly, you can assume that each individual ball is selected at random with equal likelihood of being chosen. It is common in games of chance to be rewarded for obtaining unlikely results. For example, in the game of poker, hands that are less likely to occur tend to trump hands that are more likely to occur. That same concept applies in this game. It costs $10 to play Pick-A-Ball, and your prize is the reciprocal of the probability of obtaining your exact sequence of results, expressed in dollars. For example, if the probability of obtaining your exact sequence of results is 0.10, your prize is 1/0.10

Required:
What is the probability of selecting the color of ball that you just selected?

Answer 1

The probability of selecting the color of ball that you just selected(a red ball) is
`P(r) =  (2)/(10)`

Explanation:

From the question we are told that

The total number of colored balls is n = 10

The number of red balls is r = 2 red

The number of white ball is w = 4

The number of blue balls is b = 4

The number of balls to be selected is N = 2 balls

The cost of playing picking a ball is c = $10

The winnings is
`k =  \$ P(A)`

Here P(A) is the probability of obtaining the exact sequence of result and from the question it is P(A) = 0.10

Generally my price according to the question is

`k =  (0.10 )/(10)`

=>
`k =  0.01`

Let assume we selected a red ball

Generally the probability of selecting a red ball is mathematically represented as

`P(r) =  (2)/(10)`