Dave Grace Manguilimotan

2022-03-19

Assuming that, on average, 4 out of 5 planes at Mactan International Airport arrive on schedule for a        particular time period, what is the probability that out of 8 planes, chosen at random:

1.1) all 8 planes arrive on schedule?

1.2) 5 arrive on schedule?

1.3) at least 6 arrive on schedule?

user_27qwe

$P\left(X=x\right){=}^{n}{C}_{x}{p}^{x}{q}^{n-x}$

1) Probability that all 8 planes arrive on schedule:

2) Probability that 5 planes arrive on schedule: $P\left(X=5\right){=}^{8}{C}_{5}×\left(0.{8}^{5}\right)×\left(0.{2}^{8-5}\right)=56×0.3277×0.008=0.1468$

3) Probability that at least 6 planes arrive on schedule:

$P\left(X>6\right)=P\left(X=6\right)+P\left(X=7\right)+P\left(X=8\right)$

${=}^{8}{C}_{6}×\left(0.{8}^{6}\right)×\left(0.{2}^{8-6}\right){+}^{8}C7×\left(0.{8}^{7}\right)×\left(0.{2}^{8-7}\right){+}^{8}{C}_{8}×\left(0.{8}^{8}\right)×\left(0.{2}^{8-8}\right)$

$=\left(28×0.2621×0.04\right)+\left(8×0.2097×0.2\right)+\left(1×0.1678×1\right)$

$=0.2936+0.3355+0.1678=0.7969$

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