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A bowl contains 4 red marbles and 3 yellow marbles. Tim randomly draws 3 red marbles from the bowl. He replaces each marble after it is drawn. What is the probability that he draws 2 yellow and 1 red?

Sagot :

SchwarzschildRadius
So,

The probability of drawing a yellow marble is [tex] \frac{3}{7} [/tex].
Since he replaces the marble after it is drawn out, the probability of drawing another yellow is the same: [tex] \frac{3}{7} [/tex].

The probability of drawing a red marble is [tex] \frac{4}{7}[/tex].

In order to get the probability of drawing 2 yellow marbles and 1 red marble, given that each marble is replaced after it is drawn out, we must multiply the fractions together.

[tex]( \frac{3}{7} )( \frac{3}{7} )( \frac{4}{7} ) = \frac{36}{343} [/tex]

Because the order of the marbles doesn't matter, we will multiply the probability by 3.
[tex]3( \frac{36}{343} ) = \frac{108}{343} [/tex]
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