You select a marble without looking and then put it back. If you do this 5 times, what is the best prediction possible for the number of times you will pick a marble that is not orange?
times
You select a marble without looking and then put it back. If you do this 5 times, what is the best prediction possible for the number of times you will pick a marble that is not orange?
Share
To determine the best prediction for the number of times you will pick a marble that is not orange after 5 selections, you’ll need to consider the probability of not picking an orange marble.
Assuming you know the total number of marbles and how many are orange, let’s say ( p ) is the probability of picking an orange marble, and ( 1 – p ) is the probability of picking a marble that is not orange.
If, for example, 1 out of 5 marbles is orange, then the chance of picking a marble that is not orange is ( frac{4}{5} ) or 0.8.
Thus, if you select 5 times, the expected number of times you will pick a non-orange marble is calculated by multiplying the total number of selections by the probability of not picking orange:
( 5 times (1 – p) )
If you assume an average scenario with 50% orange marbles (so ( p = 0.5 )), then:
( 5 times 0.5 = 2.5 )
However, you can’t actually pick 2.5 times in reality, so you’d typically round to either 2 or 3 as your predictions.
Ultimately, the best prediction will depend on the specific ratio of orange marbles to total marbles.
Keep in mind that the variability in outcomes means you could end up with fewer or more than your predicted number, but