You randomly draw a marble, put it back, and then randomly draw a marble.What is the probability of drawing a yellow marble and then drawing a green marble? Write answer as a fraction.
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Given:
The total number of marbles =7.
The number of yellow marbles = 2.
The number of green marbles =2.
The marbles are replaced after being drawn.
To find:
We need to find the probability of drawing a yellow marble and then drawing a green marble.
Explanation:
The probability of drawing yellow marble P(Y).
[tex]P(Y)=\frac{The\text{ number of yellow marbles}}{The\text{ total number of marbles}}[/tex][tex]P(Y)=\frac{2}{7}[/tex]The probability of drawing green marble P(G).
[tex]P(G)=\frac{The\text{ number of gr}een\text{ marbles}}{The\text{ total number of marbles}}[/tex][tex]P(G)=\frac{2}{7}[/tex]The probability of drawing a yellow marble and then drawing a green marble is
[tex]=P(Y)\times P(G)[/tex][tex]=\frac{2}{7}\times\frac{2}{7}[/tex][tex]=\frac{4}{49}[/tex]Final answer:
The probability of drawing a yellow marble and then drawing a green marble is 4/49.