Two friends, Lucy and Lydia, had just bought their first cars. Lydia uses 3 gallons of gas to drive 114 miles in her car. The gr
aph below represents the number of miles, y that Lucy can drive her car for every gallons of gas. Lucy's Gas Mileage 00 850 600 FO 500 (10,415) NEXT SLIME DO (5,207 5) 13 Gallops of Gas How many miles less doen Lydia's car travel on one gallon of gas than Lucy's car?
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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: