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Unformatted text preview: AMS 410 Actuarial Mathematics Fall 2011 Homework 1: General Probability Due Date: 09/22/2011 1. Given that P [ A B ] = 0 . 7 and P [ A B ] = 0 . 9 , find P [ A ] . 2. Given that A and B are independent, P [ A ] = 2 P [ B ] and P [ A B ] = 0 . 15 , find P [ A B ] . 3. Given that A and B are independent, P [ A B ] = 0 . 8 and P [ B ] = 0 . 3 , find P [ A ] . 4. Given that P [ A ] = 0 . 2 ,P [ B ] = 0 . 7 and P [ A | B ] = 0 . 15 , find P [ A B ] . 5. Assuming A,B and C are mutually independent, with P [ A ] = P [ B ] = P [ C ] = 0 . 1 , compute: (a) P [ A B ] (b) P [ A B C ] . 6. A mattress store sells only king, queen and twin-size mattresses. Sales records at the store indicate that one-fourth as many queen-size mattresses are sold as king and twin-size mattresses combined. Records also indicate that three times as many king-size mattresses are sold as twin-size mattresses. Calculate the probability that the next mattress sold is either king or queen-size.mattresses....
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