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need probability help

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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?

Oct 21, 2021

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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.

Oct 21, 2021