If a safety switch has a 1 in 10 chance of failing, how many switches would a company want to install in order to have only one million chance of them all failing a the same time? Show your reasoning.
If a safety switch has a 1 in 10 chance of failing, 6 switches would a company want to install in order to have only one million chance of them all failing a the same time. Failing AT THE SAME TIME, [ means that the chosen switch will have probabilities 1/10 and 1/10 and 1/10 and 1/10..... AND means multiply, therefore 1/10 * 1/10 *1/10 * 1/10 * 1/10 *1/10 = 1/1,000,000 This is also modeled by the equation: (1/10)^n = 1/1,000,000  n = 6 safety switches. ]
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