Question

round all answers to 4 decimal places.
a. a bag contains 7 blue marbles, 3 yellow marbles, and 5 black marbles. if a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a blue marble and then a black marble?
b. a bag contains 3 red marbles, 5 black marbles, and 7 yellow marbles. if two different marbles are drawn from the bag, what is the probability of drawing first a red marble and then a yellow marble?

Explanation:

Step1: Calculate total marbles in part a

Total marbles in part a = 7 + 3+ 5 = 15.

Step2: Calculate probability of drawing blue then black in part a

Since the draws are with replacement, the probability of drawing a blue marble first is $\frac{7}{15}$, and the probability of drawing a black marble second is $\frac{5}{15}$. The combined probability is $\frac{7}{15}\times\frac{5}{15}=\frac{35}{225}\approx0.1556$.

Step3: Calculate total marbles in part b

Total marbles in part b = 3 + 5+ 7 = 15.

Step4: Calculate probability of drawing red then yellow in part b

Since the draws are without replacement, the probability of drawing a red marble first is $\frac{3}{15}$, and the probability of drawing a yellow marble second (with one - less marble in the bag) is $\frac{7}{14}$. The combined probability is $\frac{3}{15}\times\frac{7}{14}=\frac{21}{210}= 0.1000$.

Answer:

a. 0.1556
b. 0.1000