Question

There are 6 blue marbles, 7 red marbles, 4 orange marbles, and 3 green marbles in a bag. Once a marble is drawn, it is replaced. What is the probability of selecting a red then a blue marble

Answer 1

The probability of an event is expressed as

`P(event)=\frac{number\text{ of desirable outcome}}{number\text{ of possible outcomes}}`

Given that:

`\begin{gathered} blue\text{ marbes:6} \\ red\text{ marbles:7} \\ orange\text{ marbles:4} \\ green\text{ marbles:3} \\ total\text{ number of marbles: 20} \end{gathered}`

This implies that the number of possible outcomes is 20.

Provided that once a marble is drawn, it's replaced, the probability of selecting a red marble then a blue marble is expressed as

`P(R\text{ and B\rparen=P\lparen red for first selection\rparen}*\text{P\lparen blue for second selection\rparen}`

where

`\begin{gathered} P(red\text{ for first selection\rparen=}\frac{number\text{ of red balls}}{total\text{ number of balls}}=(7)/(20) \\ \Rightarrow P(red\text{ for first selection\rparen=}(7)/(20) \\ P(blue\text{ for second selection\rparen=}\frac{number\text{ of blue balls}}{total\text{ number of balls left}}=(6)/(20-1) \\ \Rightarrow P(blue\text{ for second selection\rparen=}(6)/(19) \end{gathered}`

Thus, we have

`\begin{gathered} P(Red\text{ and Blue\rparen=}(7)/(20)*(6)/(19) \\ =(21)/(190) \end{gathered}`

Hence, the probability of selecting a red then a blue marble is

`(21)/(190)`