Question

finding the probability of compound events a bag contains 5 red, 4 green, and 3 blue marbles. what is the probability of randomly picking a green marble, replacing it, and then randomly picking a blue marble? 1/12 5/12 6/12 7/12

Explanation:

Step1: Calculate total number of marbles

$5 + 4+3=12$

Step2: Calculate probability of picking a green marble

The probability of picking a green marble $P(G)=\frac{4}{12}$ since there are 4 green marbles out of 12 total.

Step3: Calculate probability of picking a blue marble

Since the marble is replaced, the total number of marbles remains 12. The probability of picking a blue marble $P(B)=\frac{3}{12}$ as there are 3 blue marbles out of 12 total.

Step4: Calculate probability of compound - event

For independent events (because of replacement), the probability of both events occurring is the product of their individual probabilities. So $P = P(G)\times P(B)=\frac{4}{12}\times\frac{3}{12}=\frac{12}{144}=\frac{1}{12}$

Answer:

$1/12$