You have a bag containing 5 red markers, 6 green markers, and 4 blue markers. You reach into the bag, select 1 marker, replace it, and then select another marker. What is the probability that you selected a blue marker and then a green marker?
Question
You have a bag containing 5 red markers, 6 green markers, and 4 blue markers. You reach into the bag, select 1 marker, replace it, and then select another marker. What is the probability that you selected a blue marker and then a green marker?
Solution
To solve this problem, we need to calculate the probability of each event separately and then multiply them together because these are independent events.
Step 1: Calculate the total number of markers The total number of markers in the bag is 5 red + 6 green + 4 blue = 15 markers.
Step 2: Calculate the probability of drawing a blue marker The probability of drawing a blue marker is the number of blue markers divided by the total number of markers. So, the probability is 4 blue / 15 total = 0.2667 or 26.67%.
Step 3: Calculate the probability of drawing a green marker Since the first marker was replaced, the total number of markers remains the same. The probability of drawing a green marker is the number of green markers divided by the total number of markers. So, the probability is 6 green / 15 total = 0.4 or 40%.
Step 4: Calculate the combined probability Since these are independent events, we multiply the probabilities together to get the combined probability. So, the combined probability is 0.2667 * 0.4 = 0.1067 or 10.67%.
So, the probability that you selected a blue marker and then a green marker is approximately 10.67%.
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