Question

4. suppose a jar contains 12 red marbles and 30 blue marbles. if you reach in the jar and pull out 2 marbles at random, find the probability that both are red. (hint: is this with or without replacement?)

Answer 1

The probability of pulling out two red marbles without replacement from a jar of 12 red and 30 blue marbles is found by multiplying the probability of the first and second draws, which is (12/42) × (11/41), simplifying to 22/287 or about 0.0767.

Step-by-step explanation:

To find the probability that both marbles drawn from the jar are red, without replacement, we use the basic probability rules. Since there are 12 red marbles out of a total of 42 marbles (12 red + 30 blue), the probability of drawing the first red marble is 12/42. Once the first red marble is drawn, it is not replaced, so there are now 11 red marbles and 41 marbles total. The probability of drawing a second red marble is therefore 11/41.

To find the overall probability of both events happening (drawing two red marbles in succession without replacement), multiply the two probabilities:
(12/42) × (11/41), which simplifies to (2/7) × (11/41). Therefore, the probability of drawing two red marbles without replacement is (2/7) × (11/41), which simplifies to 22/287 or approximately 0.0767.