7. A bag contains 2 red cubes, 3 blue cubes, and 5 green cubes. If a cube is removed and replaced in the bag and another is drawn, what is the probability that both are green?
1/4
3/8
2/5
1/2
Please tell me if this is correct
1/2
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To find the probability that both cubes drawn are green, we need to calculate the probability of drawing a green cube in the first draw and then drawing another green cube in the second draw.
Step 1: Calculate the probability of drawing a green cube in the first draw:
The total number of cubes in the bag is 2 red + 3 blue + 5 green = 10 cubes.
The probability of drawing a green cube in the first draw is therefore 5 green cubes / 10 total cubes = 1/2.
Step 2: Since the first cube is replaced back into the bag, the number of cubes in the bag remains the same for the second draw.
The probability of drawing a green cube in the second draw is also 5 green cubes / 10 total cubes = 1/2.
Step 3: Calculate the probability of both events happening (drawing a green cube in the first draw and then another green cube in the second draw) occurring together by multiplying the probabilities from the previous steps.
Probability of both cubes being green = 1/2 * 1/2 = 1/4.
Therefore, the probability that both cubes drawn are green is 1/4.
Answer: 1/4.