Question

Petra has a jar full of marbles. It has 30 blue marbles and 70 red marbles. She randomly chooses one marble, replaces it and then chooses a second marble. What is the probability Petra chose two blue marbles? What is the probability Petra chose two red marbles?

Answer 1

The probability of choosing a blue marble on the first draw is 30/100 or 0.3. Since Petra replaces the first marble before the second draw, the probability of choosing a blue marble on the second draw is also 0.3. To find the probability of choosing two blue marbles, we multiply the probability of the first draw by the probability of the second draw:

P(choosing two blue marbles) = 0.3 x 0.3 = 0.09

So the probability that Petra chose two blue marbles is 0.09.

Similarly, the probability of choosing a red marble on the first draw is 70/100 or 0.7. Since Petra replaces the first marble before the second draw, the probability of choosing a red marble on the second draw is also 0.7. To find the probability of choosing two red marbles, we multiply the probability of the first draw by the probability of the second draw:

P(choosing two red marbles) = 0.7 x 0.7 = 0.49

So the probability that Petra chose two red marbles is 0.49.