Joe, who owns a grocery store, has ordered tins of chickpeas and lentils. When unpacking the tins, he finds that one box contains 10 tins that have lost their labels. The tins are identical but after looking through his invoices, he has determined that 7 of the tins contain chickpeas and 3 contain lentils. Joe decides to take them home since he is unable to sell them without a label. He will open one tin each day and use whatever it contains. Determine the probability that he opens at least one tin of each over the next 3 nights.
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Complementary counting!
Your answer is $1-P(\text{only lentils})-P(\text{only chickpeas})$.
This would then be $1-\displaystyle\frac{3}{10}\cdot\frac{2}{9}\cdot\frac{1}{8}-\frac{7}{10}\cdot\frac{6}{9}\cdot\frac{5}{8}=\boxed{0.7}$
Saketh Malyala
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Thank you Saketh. I got the same answer, but according to the textbook the solution is 5/14 – Justine Jun 09 '19 at 04:57
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