Question

probability of independent and dependent events
this quiz will test your knowledge on independent and dependent events in probability.
value: 2
a bag contains 3 blue marbles, 2 red marbles, and 5 green marbles. one marble is drawn from the bag, the color is recorded, and it is not put back into the bag. another marble is drawn and its color is recorded. what is the probability of drawing two red marbles?
○ a. 0.02
○ b. 0.04
○ c. 0.1
○ d. 0.31

1/8

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Explanation:

Step1: Calculate first - draw probability

The total number of marbles is $3 + 2+5=10$. The probability of drawing a red marble on the first draw is $\frac{2}{10}$.

Step2: Calculate second - draw probability

Since the first marble is not replaced, there are now 9 marbles left and 1 red marble left. So the probability of drawing a red marble on the second draw is $\frac{1}{9}$.

Step3: Calculate joint - probability

For dependent events, the probability of both events occurring is the product of their individual probabilities. So $P=\frac{2}{10}\times\frac{1}{9}=\frac{2}{90}\approx0.0222\approx0.02$.

Answer:

A. 0.02