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.
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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(52800) (Show Source):
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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.
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(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
