A bag contains nine blue, five red, three white, and eight green marbles. If a marble is drawn at random and replaced 75 times, determine the expected number of times a green marble could be drawn.
In this question, we’re interested in the green marbles, of which there are eight in the bag. There are 25 marbles in total as nine plus five plus three plus eight is equal to 25. This means that the probability of selecting a green marble is eight out of 25 or eight twenty-fifths. As we’re drawing a marble 75 times, we can calculate the expected number by finding eight twenty-fifths of 75 or multiplying eight over 25 by 75. Both 25 and 75 are divisible by 25. This leaves us with eight multiplied by three, which is 24. When drawing a marble 75 times from the bag, we would expect 24 to be green.
An alternative method here would be to multiply the numerator and denominator of our fraction by three. Eight multiplied by three is 24, and 25 multiplied by three is 75. Once again, we get an answer of 24 out of 75.