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 Question from rougi, a teacher: a lecturer goes to a bar because it looks like raning.he takes an umbrella with him. on the way to bar he forgets the umbrella in the bus with probability 0,1, in the bar with probability 0.3 and on his way home in the taxi with probability 0,6 a)what is probability that he forgets the umbrella on his trip? b)when he gets home he realizes that he has forgotten his umbrella,what is probability that he has forgotten it in the taxi?

Hi Rougi.

a) Rework the question backwards. What is the probability he doesn't forget his umbrella anywhere? It is 0,9 x 0,7 x 0,4. The answer to the question is the complement of this.

b) He forgot it somewhere, so the relative probabilities are what is important in this question. In this case it is relative to his forgetting his umbrella so you want to form a fraction where the denominator is the probability you calculated in part a). The numerator is the probability that when he forgot his umbrella he forgot it in the taxi. To do so he would need to not forget his umbrella on the bus AND not forget his umbrella in the bar AND forget his umbrella in the taxi. Hence the numerator is 0,9 x 0,7 x 0,6.

Cheers,
Stephen La Rocque and Harley Weston

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