QuestionGiven that Kieran saw exactly one of these types of animal, what is the probability that he saw a lion? Give your answer as a fraction in its simplest form.
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Calculate the probability that Kieran saw a lion given that exactly one type of animal was seen: - Total probability of seeing exactly one type of animal: $P(\text{Exactly One}) = P(\text{Lion and Not Rhino}) + P(\text{Rhino and Not Lion}) = \frac{1}{15} + \frac{1}{2} = \frac{1}{15} + \frac{15}{30} = \frac{2}{30} + \frac{15}{30} = \frac{17}{30}$ - Probability that Kieran saw a lion given exactly one type of animal: $P(\text{Lion} \mid \text{Exactly One}) = \frac{P(\text{Lion and Not Rhino})}{P(\text{Exactly One})} = \frac{\frac{1}{15}}{\frac{17}{30}} = \frac{1}{15} \times \frac{30}{17} = \frac{2}{17}$
The probability that Kieran saw a lion given that he saw exactly one type of animal is:
$$\boxed{\frac{2}{17}}$$