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A bag contains 6 green balls and 4 yellow balls. What is the probability that two balls picked randomly are both of the same color?

Sagot :

Given:

The number of green balls is G = 6.

The numer of yellow balls is Y = 4.

Explanation:

Determine the total number of balls.

[tex]\begin{gathered} T=6+4 \\ =10 \end{gathered}[/tex]

Determine the probability for both selected balls to be green.

[tex]\begin{gathered} P(G)=\frac{6}{10}\cdot\frac{5}{9} \\ =\frac{15}{45} \end{gathered}[/tex]

Determine the probability for selected balls to be yellow.

[tex]\begin{gathered} P(Y)=\frac{4}{10}\cdot\frac{3}{9} \\ =\frac{6}{45} \end{gathered}[/tex]

Determine the probability for both selected balls to be of same colour.

[tex]\begin{gathered} P=P(G)+P(Y) \\ =\frac{15}{45}+\frac{6}{45} \\ =\frac{21}{45} \\ =\frac{7}{15} \end{gathered}[/tex]

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