A bag has 2 red marbles, 1 blue marble and 4 gold marbles. What is the probability of drawing two gold marbles, if the first marble is replaced after it is drawn?
is it 16/49 or 7/13
To find the probability of drawing two gold marbles, given that the first marble is replaced after it is drawn, we need to calculate the probability of drawing a gold marble on the first draw and then multiply it by the probability of drawing a gold marble on the second draw, assuming that the first marble is replaced.
Let's break it down step by step:
Step 1: Calculate the probability of drawing a gold marble on the first draw:
The total number of marbles is 2 red + 1 blue + 4 gold = 7 marbles.
The probability of drawing a gold marble on the first draw is therefore 4/7.
Step 2: Calculate the probability of drawing a gold marble on the second draw, assuming the first marble is replaced:
Since the first marble is replaced, the total number of marbles remains the same at 7.
The probability of drawing a gold marble on the second draw is again 4/7.
Step 3: Multiply the probabilities from step 1 and step 2:
P(drawing two gold marbles) = P(gold on first draw) * P(gold on second draw)
= (4/7) * (4/7)
= 16/49
Therefore, the probability of drawing two gold marbles, if the first marble is replaced after it is drawn, is 16/49.
So, the correct answer is 16/49.