each draw there are 10 marbles. So,
P(pink,pink) = 3/10 * 3/10
P(pink,pink) = 3/10 * 3/10
Given that the bag has a total of 10 marbles, 2 are yellow, 3 are pink, and 5 are blue. Since the first marble is placed back in the bag before the second draw, the probability remains unaffected by previous draws.
Step 1: Calculate the probability of drawing a pink marble on the first draw:
The bag has a total of 10 marbles, out of which 3 are pink. Therefore, the probability of drawing a pink marble on the first draw is 3/10.
Step 2: Calculate the probability of drawing a pink marble on the second draw:
Since the first marble is placed back in the bag, the total number of marbles remains the same — therefore, the bag still has 10 marbles. Out of these 10 marbles, 3 are pink. Hence, the probability of drawing a pink marble on the second draw is also 3/10.
Step 3: Calculate the probability of drawing two pink marbles:
To calculate the probability of two independent events occurring, we multiply their individual probabilities. Thus, the probability of drawing two pink marbles is (3/10) * (3/10) = 9/100, which can also be expressed as 0.09 or 9%.
Therefore, the probability of drawing two pink marbles from the bag, with replacement, is 9/100, or 0.09, or 9%.
Step 1: Determine the total number of marbles in the bag after the first draw.
In this case, the total number of marbles in the bag is 10, as given in the question.
Step 2: Determine the number of pink marbles in the bag.
According to the information provided, there are 3 pink marbles.
Step 3: Calculate the probability of drawing a pink marble on the first draw.
Since there are 10 marbles in total and 3 of them are pink, the probability of drawing a pink marble on the first draw is 3/10.
Step 4: Calculate the probability of drawing a pink marble on the second draw.
Since the first marble is placed back into the bag before the second draw, there are still 3 pink marbles out of 10 marbles remaining. Therefore, the probability of drawing a pink marble on the second draw is also 3/10.
Step 5: Calculate the probability of drawing two pink marbles.
The probability of drawing two pink marbles in a row is calculated by multiplying the probabilities of each event happening. Therefore, the probability of drawing two pink marbles is (3/10) * (3/10) = 9/100.
So, the probability of drawing two pink marbles, given that the first one is placed back in the bag before the second draw, is 9/100.