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deyuntamathis
20.07.2021 •
Mathematics
The probability of a customer arrival at a grocery service counter in any one second is equal to 0.4. Assume that customers arrive in a random stream, so an arrival in any one second is independent of all others. (Round your answers to four decimal places.) (a) Find the probability that the first arrival will occur during the seventh one-second interval. 0.0187 Correct: Your answer is correct. (b) Find the probability that the first arrival will not occur until at least the seventh one-second interval.
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Ответ:
a. approximately 0.0187
b. 0.047
Step-by-step explanation:
q = 1-p
= 1-0.4
q = 0.6
a. the probability that the first arrival will occur during seventh one-second interval
probability(7) = 0.6⁷⁻¹ x 0.4
= 0.6⁶ x 0.4
= 0.046656 x 0.4
= 0.0186624
approximately 0.0187
b. probability that the first arrival will not occur until at least the seventh one second interval
p(y≥7) = 1-p(x<7)
= 1-[(0.4)(0.6)⁰ + (0.4)(0.6)¹ +(0.4)(0.6)²+(0.4)(0.6)³+(0.4)(0.6)⁴+(0.4)(0.6)⁵]
= 1-(0.4+0.24+0.144+0.0864+0.05184+0.031104
= 1-0.95334
= 0.04667
= 0.047
Ответ: