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Step-by-step explanation:

GIVEN: A bag contain $5$ red marbles, $4$ green marbles and $1$ blue marble. A marble is chosen at random from the bag and not replaced, then a second marble is chose.

TO FIND: What is the probability both marbles are green.

SOLUTION:

Total marbles in bag $=10$

total number of green marbles $=4$

Probability that first marble will be green $P(A)=\frac{\text{total green marbles}}{\text{total marbles}}$

$=\frac{4}{10}=\frac{2}{5}$

Probability that second marble will be green $P(B)=\frac{\text{total green marble in bag}}{\text{total marble in bag}}$

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As both events are disjoint

probability both marbles are green $=P(A)\times P(B)$

$=\frac{2}{5}\times\frac{1}{3}=\frac{2}{15}$

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