these marbles are placed in a bag and two of them are randomly drawn what is the probability of drawing two pink marbles if the first one is placed back in the bag before the second draw the bag has 10 marbles.2 yellow.3 pink.5 blue
To find the probability of drawing two pink marbles, we can break down the problem into two steps:
Step 1: Calculate the probability of drawing a pink marble on the first draw.
Step 2: Calculate the probability of drawing a pink marble on the second draw, assuming that the first marble was placed back in the bag.
Step 1:
In this scenario, there are a total of 10 marbles in the bag. Out of these, 3 are pink marbles. So, the probability of drawing a pink marble in the first draw would be:
P(pink on first draw) = Number of pink marbles / Total number of marbles = 3/10
Step 2:
Since we put the first marble back in the bag, the total number of marbles remains the same. However, the number of pink marbles will also remain the same, so the probability of drawing a pink marble on the second draw is still 3/10.
To find the probability of both events happening (drawing two pink marbles), we multiply the probabilities from both steps:
P(drawing two pink marbles) = P(pink on first draw) * P(pink on second draw)
= (3/10) * (3/10)
= 9/100
= 0.09
Therefore, the probability of drawing two pink marbles, with the first marble placed back in the bag, is 0.09 or 9%.
To calculate the probability of drawing two pink marbles when the first one is placed back in the bag before the second draw, we need to determine the probability of drawing a pink marble on each draw.
Step 1: Determine the number of pink marbles in the bag.
The bag contains 3 pink marbles.
Step 2: Determine the total number of marbles in the bag.
The bag contains 10 marbles in total.
Step 3: Calculate the probability of drawing a pink marble on the first draw.
P(Drawing a pink marble on the first draw) = Number of pink marbles / Total number of marbles
P(Drawing a pink marble on the first draw) = 3/10
Step 4: Since the first marble is placed back in the bag before the second draw, the probability of drawing a pink marble on the second draw will remain the same.
P(Drawing a pink marble on the second draw) = 3/10
Step 5: Calculate the probability of drawing two pink marbles.
P(Drawing two pink marbles) = P(Drawing a pink marble on the first draw) * P(Drawing a pink marble on the second draw)
P(Drawing two pink marbles) = (3/10) * (3/10)
P(Drawing two pink marbles) = 9/100
Therefore, the probability of drawing two pink marbles, with replacement, from a bag containing 10 marbles (2 yellow, 3 pink, and 5 blue) is 9/100.
there are 10 marbles, with 3 pink
so the probability of pink is 3/10
for 2 pink draws (with replacement)
...probability = .3 * .3