Question

Round all answers to 4 decimal places.

a. A bag contains 4

red marbles, 5 yellow marbles, and 7 white marbles. If a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a red marble and then a white

marble?

b. A bag contains 5

green marbles, 7 white marbles, and 4 yellow marbles. If two different marbles are drawn from the bag , what is the probability of drawing first a green marble and then a yellow marble?

Answer 1

Answer 2

Part a :-

• Total marbles: 4 (red) + 5 (yellow) + 7 (white) = 16 marbles.

• Probability of first drawing a red marble: $\frac{4}{16}$.

• Probability of then drawing a white marble (with replacement): $\frac{7}{16}$.

• Combined probability: $\frac{4}{16}\times \frac{7}{16}=\frac{28}{256}=\frac{7}{64}$.

• Decimal result: 0.1094.

Final Answer: $\boxed{{\displaystyle 0.1094}}$

Part b :-

• Total marbles: 5 (green) + 7 (white) + 4 (yellow) = 16 marbles.

• Probability of first drawing a green marble: $\frac{5}{16}$.

• Probability of then drawing a yellow marble (without replacement): $\frac{4}{15}$.

• Combined probability: $\frac{5}{16}\times \frac{4}{15}=\frac{20}{240}=\frac{1}{12}$.

• Decimal result: 0.0833.

Final Answer: $\boxed{{\displaystyle 0.0833}}$