The probabilities that Kodjo and Adoga pass an examination are \(\frac{3}{4}\) and \(\frac{3}{5}\) respectively. Find the probability of both boys failing the examination
\(\frac{1}{10}\)
\(\frac{3}{10}\)
\(\frac{9}{20}\)
\(\frac{2}{3}\)
Explanation
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For those that don't understand, let me explain
The probabilities of the two boys passing the examination are already given, but their probabilities of failures were not given:
Kodjo's success:3/4
kodjo's failure(to get his probability of failure, you subtract 1 from his probability of success or passing the exam and vice versa)
i.e kodjo's failure:1-probability of success
i.e 1-3/4=1/4
Adoga's success:3/5
Adoga's failure:1-3/5=2/5
Now that you've gotten their probabilities of failure, you can proceed to the question:
Probability of both boys failing the examination
To do this, all you have to do is to multiply their failures (which you've just gotten)
So,
Probability of both boys failing the examination:1/4 ×2/5=2/10 and reducing to lowest terms gives 1/10
so the answer is 1/10
