Two different 2-digit numbers are randomly chosen and multiplied together. What is the probability that the resulting product is a multiple of 5?
The answer will be a multiple of 5 if one, or both, of the numbers ends in 0 or 5.
There are 90 numbers in total and 18 of them end in 0 or 5
The prob that the first one is a multiple of 5 and the second one is not is \(\frac{18}{90}*\frac{72}{89}=\frac{72}{445}\)
The prob that the first one is not a multiple of 5 and the second one is will be the same 72/445
The prob that they are both multiples of 5 is \(\frac{18}{90}*\frac{17}{89}=\frac{17}{445}\)
P(that the multiple will be a multiple of 5) = \(\frac{2*72+17}{445}=\frac{161}{445}\)
You need to check for careless errors.