SOLUTION: Two numbers a and b, are randomly selected without replacement from the set {2,3,4,5,6,7}. What is the probability that the fraction a/b is lessthan 1 and can be expressed as a ter

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Question 157692: Two numbers a and b, are randomly selected without replacement from the set {2,3,4,5,6,7}. What is the probability that the fraction a/b is lessthan 1 and can be expressed as a terminating decimal?
Could you please explain this, Please?
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
To find the probability that a%2Fb is less than 1 and can be expressed as a terminating decimal, simply list all of the fractions where a%3Cb (since the fraction must be less than 1) and take note which ones have terminating decimals

2%2F3=0.667 (non terminating), 2%2F4=1%2F2=0.5 (terminating), 2%2F5=0.4, 2%2F6=0.333 (non terminating), 2%2F7=0.286 (non terminating), etc...


It turns out that there are 3 different possible combinations of a%2Fb. So count the number of terminating decimal fractions a%2Fb and this will form the numerator while the total number of combintations (30) will form the denominator.


Let me know if you need more help.