There are 5 red cubes and 10 green cubes in a bag. A cube is picked then put back in the bag and another is chosen. If I did this is done 180 times, how many green cubes would you expect to have picked?
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To calculate the expected number of green cubes picked, we need to find the ratio of the number of green cubes to the total number of cubes in the bag.
In this case, there are 10 green cubes and 5 red cubes, making a total of 15 cubes in the bag. Therefore, the probability of picking a green cube is 10/15, or 2/3.
Since each pick is independent and we are picking 180 times with replacement (putting back the cube after each pick), we can multiply the probability of picking a green cube (2/3) by the number of picks (180) to find the expected number of green cubes picked.
Expected Number of Green Cubes = (Probability of picking a green cube) x (Number of picks)
= (2/3) x 180
= 120
Therefore, you would expect to have picked 120 green cubes after performing this process 180 times.