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Mathematics 1050 Some solutions of Homework 5 An unbiased coin is tossed ve times. Find the probability of the event that the coin lands heads exactly once. Section 7.4: 2 Solution: Each outcome of the experiment can represented as a sequence of heads and tails. Using the multiplication principle, we see that the number of outcomes of this experiment is given by 2 . Let E denote the event that the coin lands heads exactly once. Since there are C (5; 1) ways this can occur, we see the required probability is 5 5 ( ) C (5; 1) = = = : n(S ) 2 32 32 4 Find the probability that the coin lands heads more than once. ( )= P E Section 7.4: 5! n E 4! 5 Let F denote the event that the coin lands heads more than once. Then, F c is the event that the coin does not land heads, which means that it lands tails ve times. There are C (5; 5) ways that this occur. Hence Solution: ( P F c )= ( c) = n(S ) n F C (5; 5) 1 = : 2 32 5 On the other hand 1 31 = : 32 32 Section 7.4: 10 Four balls are selected at random without replacement from an urn containing 3 white balls and 5 blue balls. Find the probability that they are all blue. ( )=1 P F ( P F c )=1 We have a total of 8 balls. The number of outcomes of this experiment is C (8; 4). denote that the event that the 4 balls are blue. Then Solution: Let E ( )= P E 1 (5; 4) 5 4 3 2 = = : C (8; 4) 8 7 6 5 14 C 1