Events A1, Az and A3 form a partiton of the sample space S with probabilities P(A¡) = 0.2, P(A2) = 0.3, P(A3) = 0.5. If E is an event in S with P(E|A1) = 0.5, P(E|A2) = 0.4, P(E|A3) = 0.8, compute %3D P(E) = 1 P(A||E) 0.5 P(A2|E) = 0.6 P(A3|E) : 0.2

1 Rank the probabilities of 10%, 5, and 0.06 from the most likely to occur to the least likely to occur. O a Ob O c Od 1 0.06, 5, 10% 1 5, 10%, 0.06 1 10%, 5, 0.06 0.06, 10%, 5

Compute the z-scores and the population probabilities for these normally distributed events: a) mx = 96, sx = 14, z = _______ P(x < 81) = _____________ b) mx = 0.42, sx = 0.11, z = _______ P(x > 0.60) = _____________ c) mx = 1250, sx = 850, z = _______ P(x > 650) = _____________ d) mx = 9.0, sx = 3.4, z = _______ P(x < 11.8) = _____________

An experiment consists of rolling a weighted die. The probability of rolling each number is: Pr[1]=0.25Pr[1]=0.25, Pr[2]=0.1Pr[2]=0.1, Pr[3]=0.15Pr[3]=0.15, Pr[4]=0.25Pr[4]=0.25, Pr[5]=0.2Pr[5]=0.2, and Pr[6]=0.05Pr[6]=0.05. On the first roll, you record if the number is Small (1,2,3) or Large (4,5,6). If the first number is Small, then on the second roll you record if the number is a 2 or not. If the first number is Large, on the second roll you record whether the number is Small or not. So, some typical outcomes would be S2 (small number rolled, then 2) or LL (large number rolled, then another large number). Draw a tree diagram and use it to answer the following questions. (1) What is Pr[S2]? (2) What is Pr[LL]?

An experiment can result in one of five equally likely simple events, E₁, E₂, A: E₂, E4 2' P(A) = = 0.4 B: E₁, E3, E4, E5 P(B) = 0.8 C: E₂, E3 Refer to the following probabilities. P(A n B) = 0.2 P(AIB) = 0.25 P(BIA) P(BU C) = 1 P(BIC) 0.5 P(CIB) 0.25 Use the Addition and Multiplication Rules to find the following probabilities. (a) P(AUB) (b) P(An B) = 0.5 P(A U B) = ---Select--- + ---Select--- ✓ P(A n B) = ---Select--- (c) P(B n C) Yes P(B n C) = ---Select--- No P(C) = 0.4 . P(B) = = P(C) = = ---Select--- V = Do the results agree with those obtained by listing the simple events in each? P(A U B) = P({E₁, E₂, E3, E4, E5}) = 1 P(A n B) = P({E₁}) = 0.2 P(B n C) = P({E3}) = 0.2 .., E5. Events A, B, and C are defined as follows.

An experiment consists of rolling a weighted die. The probability of rolling each number is: Pr[1]=0.05Pr[1]=0.05, Pr[2]=0.25Pr[2]=0.25, Pr[3]=0.1Pr[3]=0.1, Pr[4]=0.15Pr[4]=0.15, Pr[5]=0.2Pr[5]=0.2, and Pr[6]=0.25Pr[6]=0.25. On the first roll, you record if the number is Small (1,2) or Large (3,4,5,6). If the first number is Small, then on the second roll you record if the number is a 1 or not. If the first number is Large, on the second roll you record whether the number is Small or not. So, some typical outcomes would be S1 (small number rolled, then 1) or LL (large number rolled, then another large number). Draw a tree diagram and use it to answer the following questions. (1) What is Pr[S1]? (2) What is Pr[LL]?  (3) What is Pr[(not1)onsecondroll|Sonfirstroll]? (4) What is Pr[S on second roll|L on first roll]?

What is the probability of getting at least a 3 star review, P(x≥3) ?