if a bag contains 6 red and 4 blue marbles and one is taken out and not put back and another is taken out
is the problility that both are red
The probability for the first is 6/10 (3/5).
The probability for the second is 5/9.
Multiply them for your answer, 1/3.
6/10 * 5/9 = 30/90 = 1/3
To find the probability that both marbles drawn are red, we can use the concept of conditional probability.
Step 1: Determine the probability of drawing a red marble on the first draw.
The bag contains a total of 6 red and 4 blue marbles, so the probability of drawing a red marble on the first draw is 6/10.
Step 2: Calculate the number of red marbles remaining after the first draw.
Since one marble was taken out and not put back, there are now a total of 9 marbles left in the bag (6 red and 3 blue).
Step 3: Determine the probability of drawing a red marble on the second draw, given that the first marble drawn was red.
With 6 red marbles left out of a total of 9 marbles, the probability of drawing a red marble on the second draw is 6/9.
Step 4: Compute the probability of both marbles being red.
To find the probability of two independent events occurring together, we multiply their individual probabilities. Hence, the probability of drawing two red marbles in succession is (6/10) * (6/9) = 36/90 = 2/5.
Therefore, the probability that both marbles drawn are red is 2/5 (or 0.4 or 40%).