



 
Hi Peter, The probability of a single event, such as choosing a multiple of 4, can be found by the simple probability formula: # of successful outcomes = 100 since every 4th number is a multiple of 4 = 1/4 The probability of choosing a multiple of 17 can be found in the same way: # of successful outcomes = 23 since every 17th number is a multiple of 17 ** ** to find how many multiples of 17 are less than or equal to 400, with or without a calculator, simply divide 400 by 17 to see how many times it goes in, ignoring any remainder you may get. If we need to want the probability that the number is a multiple of 4 OR a multiple of 17, we must use the OR Probability Formula: P(A or B) = P(A) + P(B)  P(A and B) If we let A be the event that we choose a multiple of 4, and B be the event that we choose a multiple of 17, then (A and B) would be the event that the number is a multiple of 4 and a multiple of 17 at the same time. Since 4 and 17 have no common factors (as 17 is prime), all numbers that are multiples of both will be multiples of their product (4*17=68) There are 5 multiples of 68 less than or equal to 400 (found like ** above for 17). Therefore, P(A or B) = 100/400 + 23/100  5/100 = 118/400 = 59/200 in lowest terms. Hope this helps,  


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