Suppose that 28% of people own a cool hat. If I randomly select 20 people, how likely am I to find that exactly 4 of them have a cool hat? What is the probability that more than 4 have a cool hat? What is the probability that between 4 and 7 (inclusive) have a cool hat?
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To evaluate a binomial probability on your calculator, press [2nd] then [VARS] to select DISTR and scroll down to binompdf or binomcdf and press [ENTER]. The syntax is binompdf(n,p,x), where n is the number of trials, p is the probability of success, and x is the desired number of successes.
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? To calculate exact probabilities, use binompdf. For example, if there are 10 trials, each with probability .75 of success, the probability of exactly 5 successes is binompdf(10, .75, 5).
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? To calculate “at most” probabilities, use binomcdf. For example, if there are 10 trials, each with probability .75 of success, the probability of at most 5 successes is binomcdf(10, .75, 5).
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? To calculate “at least” probabilities, use the complement of the above strategy for “at most.” For example, the complement of “at least 6 successes” is “fewer than 6 successes.” Therefore, P(at least 6) = 1 − P(fewer than 6) = 1 − P(at most 5).
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? In any case, always ask yourself: “What is n? What is p? What is x?” Your success on binomial problems requires three important skills: identifying binomial experiments, finding these three numbers correctly, and using the correct command on your calculator. In other words:
– when to use a binomial command – what numbers to put into it
– which binomial command to use
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Suppose that 28% of people own a cool hat. If I randomly select 20 people, how likely am I to find that exactly 4 of them have a cool hat?
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What is the probability that more than 4 have a cool hat?
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What is the probability that between 4 and 7 (inclusive) have a cool hat?
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If I flip 100 fair coins, how likely am I to get exactly 50 Heads and 50 Tails?
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If I roll a fair die 100 times, how likely am I to get at least 12 6s?
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