There are 4 quarters, 1 dime, and 4 nickels in a drawer. An experiment consists of selecting a coin at random, noting its value and setting it aside. If it is a dime, the experiment ends. If it is not a dime, then one more coin is selected at random, and its value is noted. Find the probability that at least 1 quarter is selected.
Total number of coins when the first coin is selected
= (4+1+4)= 9.
Number of coins when the second coin is selected = 9-1 = 8
The probability tree is shown in the attached image.
Here, sample space S consists of all the paths through the tree, while the eventspace, E, consists of those outcomes through which at least a quarter, Q is drawn. The event space is labelled (E) in the attached image.
Therefore, P(E)= `4/9*3/8+4/9*1/8+4/9*4/8+4/9*4/8`
Therefore, the probability that at least one quarter is selected in the given experiment is `2/3`.