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Question
Tickets are numbered from 1 to 10. Two tickets are drawn one after the other at random. Find the probability that the number on one of the tickets is a multiple of 5 and on the other a multiple of 4.
Solution
\[ \text{ We know that 5 and 10 aremultiples of 5, while 4 and 8 are multiples of 4 } .\]
\[P\left( \text { multiple of 5 }\right) = \frac{2}{10} = \frac{1}{5}\]
\[P\left( \text{ multiple of 4 } \right) = \frac{2}{10} = \frac{1}{5}\]
\[P\left( \text{ multiple of 5 and multiple of 4 } \right) = P\left( \text{ multiple of 5 on first card and multiple of 4 on second card } \right)\]
\[ + P\left( \text{ multiple of 4 on first card and multiple of 5 on second card } \right)\]
\[ = \frac{2}{10} \times \frac{2}{9} + \frac{2}{10} \times \frac{2}{9} \left[ \text{ Without replacement } \right]\]
\[ = \frac{4}{90} + \frac{4}{90}\]
\[ = \frac{8}{90}\]
\[ = \frac{4}{45}\]
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