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Sagot :
Solution:
The probability of an event is expressed as
[tex]P(event)=\frac{number\text{ of desirable outcome}}{number\text{ of possible outcomes}}[/tex]Given that:
[tex]\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}[/tex]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
[tex]P(R\text{ and B\rparen=P\lparen red for first selection\rparen}\times\text{P\lparen blue for second selection\rparen}[/tex]where
[tex]\begin{gathered} P(red\text{ for first selection\rparen=}\frac{number\text{ of red balls}}{total\text{ number of balls}}=\frac{7}{20} \\ \Rightarrow P(red\text{ for first selection\rparen=}\frac{7}{20} \\ P(blue\text{ for second selection\rparen=}\frac{number\text{ of blue balls}}{total\text{ number of balls left}}=\frac{6}{20-1} \\ \Rightarrow P(blue\text{ for second selection\rparen=}\frac{6}{19} \end{gathered}[/tex]Thus, we have
[tex]\begin{gathered} P(Red\text{ and Blue\rparen=}\frac{7}{20}\times\frac{6}{19} \\ =\frac{21}{190} \end{gathered}[/tex]Hence, the probability of selecting a red then a blue marble is
[tex]\frac{21}{190}[/tex]
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