Suppose a jar contains 6 red marbles and 29 blue marbles. If you reach in the jar and pull out 2 marbles at random without replacement, find the probability that both are red. Give your answer as a fraction or decimal out to at least 4 places.
Question
Suppose a jar contains 6 red marbles and 29 blue marbles. If you reach in the jar and pull out 2 marbles at random without replacement, find the probability that both are red. Give your answer as a fraction or decimal out to at least 4 places.
Solution
To solve this problem, we need to use the concept of probability.
Step 1: Calculate the total number of marbles. The total number of marbles in the jar is the sum of the red marbles and the blue marbles. So, we have 6 red marbles + 29 blue marbles = 35 marbles.
Step 2: Calculate the probability of drawing the first red marble. The probability of drawing a red marble on the first draw is the number of red marbles divided by the total number of marbles. So, the probability is 6/35.
Step 3: Calculate the new total number of marbles after one has been drawn. After drawing one marble, we are left with 34 marbles in the jar.
Step 4: Calculate the probability of drawing the second red marble. Now, we have 5 red marbles left and the total number of marbles is 34. So, the probability of drawing a red marble on the second draw is 5/34.
Step 5: Calculate the probability of both events happening. The probability of both events happening is the product of the probabilities of each event. So, the probability of drawing two red marbles in a row is (6/35) * (5/34) = 0.0254 or 2.54%.
So, the probability that both marbles drawn are red is approximately 0.0254 or 2.54%.
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