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Two different 2-digit numbers are randomly chosen and multiplied together. What is the probability that the resulting product is a multiple of 5?

 Apr 17, 2021
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We  have  90 *89   possible outcomes  (some   are the same)  =  8010 possible outcomes

 

The two-digit multiples  of 5  are

 

10   15   20   25  30 35 40  45  50  55  60  65   70  75  80  85   90  95    =  18 total

 

The only  way  to get  a multiple of  5  is either

 

!) choose one of  these multiples of  5 and  any other two-digit number that isn't a multiple of 5 =

 

(18)  ( 89  - 17 )  = (18)  (72)  =  1296   possibilities 

 

2) choose  any two of  the multiples of 5  = C(18,2)   =  153  possibilities

 

So...the probability of  a  multiple of 5  is    (  1296+ 153) / 8010  ≈  .18  =  18%

 

 

cool cool cool

 Apr 17, 2021

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