Sandy is helping her uncle at this coffee shop. She observes that, when ordering coffee, 13 of customers select chocolate flavor
ing. To simulate the behavior of the next 5 customers, she lets the number 1 represent someone ordering chocolate, and she lets the numbers 2 or 3 represent someone ordering a different flavor. She writes the numbers 1, 2, and 3 on cards and mixes them up. Sandy then picks one card, records the result, and puts the card back. She does this process four more times to represent 5 customers and to complete 1 trial of the experiment. She repeats this experiment for a total of 10 trials. The results are recorded in the table. 12323 13123 22222 23111 11322 31112 23331 11231 32332 13111 Using this simulation, what is the probability that 3 or more of the next 5 customers will order chocolate? Enter your answer, as a fraction in simplified form, in the box.
2 answers:
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The integrals over B and T will be positive. Keeping fixed,
is strictly increasing over D as
increases, so the integrals over
(i.e. the bottom/top left quadrants of D) is negative but the integrals over
are *more* positive.
The integrals over R and L are zero. If we take , then
, which is to say
is symmetric across the
-axis. For the same reason, the integral over all of D is also zero.