Question

A box contains 4 Red and 3 white balls. Everytime one ball is drawn randomly and is placed back along with two more balls of opposite colour. What is the probability that among the first 3 trials in first two one get red colour ball and in 3rd he ger white ball.

Answer 1

DEFINITION AND FORMULA

The formula for calculating the probability of an event E happening is given to be:

`P(E)=\frac{n(E)\text{ }}{N}`

where n(E) is the number of times event E happened and N is the total number of times all the events occurred.

If we are to combine probabilities, that is calculating the probability of multiple scenarios, we will multiply the probabilities together.

SOLUTION

The box contains 7 balls in total: 4 red balls and 3 white balls. After every draw, 2 balls of the opposite colour are added.

First Draw: Red ball is drawn (4 red, 3 white)

`P=(4)/(7)`

Second Draw: Red ball is drawn (4 red, 5 white)

`P=(4)/(9)`

Third Draw: White ball is drawn (4, 7 white)

`P=(7)/(11)`

Combined Probability:

`\begin{gathered} P=(4)/(7)*(4)/(9)*(7)/(11) \\ P=(16)/(99) \end{gathered}`

ANSWER

The correct option is OPTION B.