6. Rectangle ABCD is shown above. AB = 3x+8, and CD = 2x+13. Find x.
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This kind of experiments are ruled by Bernoulli's formula. If you have probability p of "success", and you want k successes in n trials, the probability is
It's easier to compute the first probability by difference: instead of computing the probability of the event "at least one of the surveyed eats breakfast", let's compute the probability of its contrary: none of them eats breakfast. So, we want 0 successes in 4 trials, with probability of success 0.34. The formula yields
Since the contrary has probability 17%, our event "at least one of the surveyed eats breakfast" has probability 83%.
As for the second question, the event "at least three of the surveyed eats breakfast" is the union of the events "exactly three of the surveyed eats breakfast" and "exactly four of the surveyed eats breakfast". So, we just need to sum their probabilities: