The probabilities that John and James pass an examination are \(\frac {3}{4}\)and \(\frac {3}{5}\) respectively. Find the probability of both boys failing the examination.
To find the probability of both John and James failing the examination:
Probabilities of failing:
\(P(\text{John fails}) = 1 - P(\text{John passes}) = 1 - \frac{3}{4} = \frac{1}{4}\)
\(P(\text{James fails}) = 1 - P(\text{James passes}) = 1 - \frac{3}{5} = \frac{2}{5}\)
Probability of both failing:
\(P(\text{Both fail}) = P(\text{John fails}) \times P(\text{James fails}) = \frac{1}{4} \times \frac{2}{5} = \frac{2}{20} = \frac{1}{10}\)
Thus, the probability of both boys failing the examination is:
\(\frac{1}{10}\)
There is an explanation video available below.
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