SOLUTION: A jar contains 5 pennies, 5 nickels and 5 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. R

Question 1206739: A jar contains 5 pennies, 5 nickels and 5 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins.
Round your answers to 3 decimal places.
Find the probability X = 10.
Find the probability X = 11.
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.
A jar contains 5 pennies, 5 nickels and 5 dimes.
A child selects 2 coins at random without replacement from the jar.
Let X represent the amount in cents of the selected coins.
Round your answers to 3 decimal places.
(a) Find the probability X = 10.
(b) Find the probability X = 11.
~~~~~~~~~~~~~~~~~~~

(a)  The number of all possible permutations of 5+5+5 = 15 coins taken by 2 at a time is total 15*14 = 210.

     The number of all favorable permutations giving the sum of X= 10 cents is favorable = 5*4 = 20
     ( any one 5c coin and other 5c coin in any order).

     The probability of success is  P =  =  = 0.095  (rounded as requested).   ANSWER



(b)  is very similar to (a), but there are some differences.  The total permutations of two coins is 15*14 = 210 
     different pairs of two coins.

     Favorable are the all the pairs  11c = 10c + 1c = 1c + 10c.  The number of such pairs/(permutations) is 5*5 + 5*5 = 25+25 = 50. 

     The probability of success is  P = {{50/210}}} =  = 0.238  (rounded as requested).   ANSWER

Solved.

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