A bag contains 7 red marbles and 5 yellow marbles. What is the probability of drawing a red marble, replacing it in the bag and then drawing a red marble once again on the second try?
Answer – The combined probability of drawing a red marble, replacing it and then drawing a red marble once again is or 0.405.
Explanation:
The number of red marbles = 7
The number of yellow marbles = 5
The total number of marbles in the bag = 7+5 = 11
If the first time a red marble is drawn from the bag is labeled event A, its probability is expressed as P(A).
Here, P(A) = []
The second time a red marble is drawn can be called event B.
Here, since the red marble is replaced after A, there is no change in the composition of marbles in the bag. There continue to be 7 red marbles and a total of 11 marbles.
Thus, P(B) =
The occurrence of A has had no effect on the occurrence of B. The two are, thus, independent events. In order to calculate their combined probability, the two must be multiplied.
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