Question

Suppose a jar contains 8 red marbles and 26 blue marbles. You reach in the jar and pull out two marbles without putting them back in. What is the probability that you would pull out a red marble followed by another red marble.

Answer 1

To calculate the probability of drawing two red marbles in a row without replacement from a jar with 8 red and 26 blue marbles, multiply the probabilities of drawing each marble consecutively: (8/34) * (7/33), simplifying to 4/81.

Step-by-step explanation:

The question involves calculating the probability of pulling out a specific sequence of marbles from a jar, which is a typical problem in probability theory and combinatorics. Given a jar containing 8 red marbles and 26 blue marbles, to find the probability that you would pull out a red marble followed by another red marble without replacement, we use the following approach:

1. Calculate the probability of drawing the first red marble.
2. Then calculate the probability of drawing a second red marble given that the first marble pulled was red and was not replaced.
3. Multiply the probabilities from step 1 and step 2 to find the overall probability of drawing two red marbles in sequence without replacement.

The probability of drawing the first red marble is 8 out of the total number of marbles, which is 34. So, P(Red1) = 8/34.

After removing one red marble, there are now 33 marbles left in the jar, of which 7 are red. Thus, the probability of drawing a second red marble is 7 out of 33. So, P(Red2 | Red1) = 7/33.

Finally, we multiply these two probabilities to get the total probability of drawing two red marbles in a row without replacement. P(Red1 and Red2) = (8/34) * (7/33) = 56/1122, which simplifies to 4/81.