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
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- Traffic is if the percentage of sound units in the production of a type of signal lamp is 80% and the number of units follows the Poisson distribution. If we draw a random sample of ten lamps, then the probability of getting two idle lamps is ............. ... the most isMiami Beach Medical Clinic (MBMC) has about 17.5 patients arriving per hour on average. MBMC serves about 20 patients per hour on average. Also, MBMC does NOT follow the traditional M/M/1 model. A patient arriving at this facility is expected to have one of the following wait times of (0 or 1 or 4 or 6 or 8 minutes) in the queue before being served. The probabilities associated with these wait times in the queue are 0.3, 0.2, 0.3, 0.1, and 0.1 respectively. The patient’s average wait time in queue is expected to be: a. 2.3 minutes b. 7.2 minutes c. 5.6 minutes d. 3.9 minutes e. 2.8 minutesSuppose there is a 14.1% probability that a randomly selected person aged 30 years or older is a smoker. In addition, there is a 25.4% probability that a randomly selected person aged 30 years or older is male, given that he or she smokes. What is the probability that a randomly selected person aged 30 years or older is male and smokes? ea PPO Fir The probability that a randomly selected person aged 30 years or older is male and smokes is (Round to three decimal places as needed.). ja ai ee lin
- Q2. (a) A construction company receives 68% of its ready mix concrete from supplier A and the remainder is supplied by supplier B. From records of previous consignments, it is known that the probability that the ready mix concrete from supplier A is of low quality and needs to be returned is 0.03, while the probability that the ready mix concrete from supplier B needs to be returned is 0.06. ) Display these probabilities on a tree diagram. (i) Calculate the probability that a consignment of ready mix concrete delivered to the construction company is of low quality and needs to be returned. (ii) Given that a consignment of ready mix concrete needs to be returned, calculate the probability that it was supplied by supplier A. (b) A company is tendering for 6 new contracts. Penalties will be applied if any of the contracts are not completed on time. The cost due to not completing a contract on time must be accounted for in the tender price. In recent years, this company has completed 20…The probabilities of events E, F, and EnF are given below. Find (a) P(EIF), (b) P(FIE), (c) P (EIF'), and (d) P (FIE'). 1 P(E) = ₁ P(F) = —, P(ENF) = =1/11 a. P(EIF) = (Type an integer or a simplfied fraction.) b. P(FIE) = (Type an integer or a simplfied fraction.) C. P (EIF') = (Type an integer or a simplified fraction.) d. P (FIE') = (Type an integer or a simplfied fraction.)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
- A system consists of four parts that work independently of each other. Working probabilities of these parts are given as 0.9 , 0.8 , 0.7 and 0.6, respectively. If the random variable X is defined as the total number of parts working in this system, calculate the probabilities P {X>0}, P {X=2} , the expected value and the variance.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) ?
