Assume that a box contains four red jelly beans and two green ones. We consider the event that a red bean is drawn. Now suppose I pick a jelly bean from the same box without looking, but I do not put the bean back in the box. Then I choose a bean again.
What is the probability of getting two red beans?
The probability of getting a red bean on the first draw is 4/6 (since there are 4 red and 2 green beans initially).
After the first bean is removed, there are only 5 beans left in the box (3 red and 2 green). Therefore, the probability of drawing a red bean on the second draw, given that a red bean was not replaced, is 3/5.
To calculate the probability of getting two red beans in a row, we can multiply the probabilities of each step:
Probability of getting a red bean on the first draw = 4/6
Probability of getting a red bean on the second draw, without replacement = 3/5
Therefore, the probability of getting two red beans in a row is:
(4/6) x (3/5) = 2/5 or 0.4
So, there is a 40% chance of drawing two red jelly beans in a row from this box without replacement.