## Elementary Statistics (12th Edition)

a) $P(X=5)={6\choose 5} \cdot (0.2)^5\cdot (0.8)^1=0.001536.$ b)$P(X=6)={6\choose 6} \cdot (0.2)^6\cdot (0.8)^0=0.000064.$ c)$P(X\geq5)=P(X=5)+P(X=6)={6\choose 5} \cdot (0.2)^5\cdot (0.8)^1+{6\choose 6} \cdot (0.2)^6\cdot (0.8)^0=0.001536+0.000064=0.0016$ d) Yes, it is an unusually low probability, because 0.0016 is really low, lower than 0.05.