Homework Help

There are 4 quarters, 1 dime, and 4 nickels in a drawer.  An experiment consists of...

user profile pic

cbromm | (Level 1) Honors

Posted June 28, 2013 at 9:53 PM via web

dislike 1 like

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.

1 Answer | Add Yours

user profile pic

llltkl | College Teacher | (Level 3) Valedictorian

Posted June 29, 2013 at 2:27 AM (Answer #1)

dislike 1 like

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`

= `4/9(3/8+1/8+4/8+4/8)`

=`4/9*12/8`

=`2/3`

Therefore, the probability that at least one quarter is selected in the given experiment is `2/3`.

Images:
This image has been Flagged as inappropriate Click to unflag
Image (1 of 1)

Sources:

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes