# STAT230 Study Guide - Midterm Guide: Decimal Mark, Blood Test

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Short Solutions to Stat 230 Test 2, Feb 1, 2012

1. An irregular die is loaded to give the probabilities P({1}) = 0.2, P({2}) = 0.4, P({3}) = P({4}) =

P({5}) = P({6})=0.1. The die is rolled 8 times and results from diﬀerent rolls are independent.

Find the probability that

[2] (a) A = “1 does not occur”

P(A) = (1 −0.2)8= 0.88= 0.1678

[1] (b) B = “2 does not occur”

P(B) = (1 −0.4)8= 0.68= 0.0168

[2] (c) C = “neither 1 nor 2 occurs”

P(C) = P(AB) = (1 −0.2−0.4)8= 0.48= 0.00066

[2] (d) D = “both 1 and 2 occur”

P(D) = P(¯

A¯

B)=1−P(A∪B) = 1 −[P(A) + P(B)−P(AB)] = 1 −(0.88+ 0.68−0.48) = 0.8161