By F M Dekking; et al

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**Extra info for A modern introduction to probability and statistics : understanding why and how**

**Sample text**

2. The law of total probability (illustration for m = 5). 2). Another, perhaps more pertinent, question about the BSE test is the following: suppose my cow tests positive; what is the probability it really has BSE? Translated, this asks for the value of P(B | T ). The information we were given is P(T | B), a conditional probability, but the wrong one. We would like to switch T and B. 2): 1 We choose this probability for the sake of the calculations that follow. The true value is unknown and varies from country to country.

2 A fair die is thrown twice. ” a. Calculate P(A | B). b. Are A and B independent events? 3 We draw two cards from a regular deck of 52. ” a. Compute P(S1 ), P(S2 | S1 ), and P(S2 | S1c ). b. Compute P(S2 ) by conditioning on whether the ﬁrst card is a spade. 10. 3 · 10−5 . Compute P(B | T ) and P(B | T c). 5 A ball is drawn at random from an urn containing one red and one white ball.

What is the probability that he will reach B after two selections? A • ....... .. ....... .............. ........ ....... . . . . .... .... ...... .......... . . . .... ... . ..... . . .... ... .. .... . . .... . .... . . . . . .... .... . . . . . . ..... . 2 A fair die is thrown twice. ” a. Calculate P(A | B). b. Are A and B independent events? 3 We draw two cards from a regular deck of 52. ” a. Compute P(S1 ), P(S2 | S1 ), and P(S2 | S1c ). b. Compute P(S2 ) by conditioning on whether the ﬁrst card is a spade.