Let N be the number of the events A1, A2,..., An which occur. Show that n E(N) = P(A;). i=1
Q: given that P(E) = 0.8, what must be true about the event E? a) event E is impossible b) event E is…
A: Given that P(E)=0.8 0.8 is very close to 1.
Q: Twelve fair die are rolled. Let X be the sum of the die rolls. Find P(X = 60 |X > 58). %3D
A: Since you have asked multiple questions, we will solve the first question for you. If you want any…
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A: given data P( drives a car) = 0.757P(use public transport) = 0.083
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Q: Let Ar, r ≥ 1, be events such that P(Ar) = 1 for all r. Show that P(1 Ar) = 1.
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Q: Be sure to keep up to 4 decimal places for all answers Suppose that P(A)=1/4 and P(B)=1/3. Assuming…
A: P(A) = 14P(B) = 13mutually exclusive events.
Q: 5. A certain drugstore has three public telephone booths. For i = 0, 1, 2, 3, let p; denote the…
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Q: Let B1, ... , Bn be independent events. Show n n P(ÜB.) = 1- T1c (1— Р(B,)). i=1 1=1
A: P∪I=1nBi=1-∏i=0n1-PBi For n =1 R.H.S=1-(1-PB1)=1-1+PB1=PB1=L.H.S For n = 2…
Q: find P( F and S) find P(F|S)
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Q: Let A, and A, be two events such that P[A] = 1/2. P[A2] = 3/5 and P[A2|A1] = 2/5 Then: %3D O PLA, n…
A: Solution: From the given information,
Q: Using the table provided, suppose that E is the event that a new car buyer intends to drive her/his…
A: Number of milesFrequencyFewer than 250001725001-75005675001-12500087125001-17500031175001 or more9
Q: According to an article, 37% of adults have experienced a breakup at least once during the last 10…
A: n = 9, p = 37% = 0.37Let X be the number of adults have experienced a breakup at least once during…
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Q: 3. For two events A and B, the probability that A occurs is 0.8, the probability that B occurs i…
A: Given that there are two events A and B such thatThe probability that A occurs is 0.8.The…
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A: According to the given information,Probability of success, p = 49% = 0.49Sample size, n = 9So,…
Q: Q 2 / b/ Suppose that the following probabilities for the two events A and B are as follows: P (A) =…
A: Given data is ,P(A)=0.5P(B)=0.7P(A∪B)=0.85
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A: Given: P(H) = 0.2 , P(R) = 0.4 ,Probability that events H and R occur = P( H ∩ R) = 0.1Probability…
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Q: Test { (-1,"! (n! (2m)!
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Q: The following table of 850 students shows those that have or don’t have covid-19 and shows those who…
A: Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a…
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A: In question, We'll select the correct option. The explanation is below,
Q: If Aj, j = 1, 2,..., n are independent events, show that (equation in picture)
A: If are independent events , then we have to show that
Q: 1. Find the following probabilities (a) P(x 2) when n8.p-0.3, (b) P(x 9) when n (c) P(x 0) when n…
A: hereX~Binomial distributionPX=x=nCxPx 1-Pn-x
Q: 2) Given X-N (10,9), find the probability for P (9.25 ≤ x ≤12.25)
A: X~N(10,9) Mean(μ)=10 standard deviation(σ)=9
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A: Since we know that Independent events : The outcomes of first events does not affect the outcomes of…
Q: n! ≥ 3n, n = 7, 8,....
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Q: T: at most two coins show Heads. Find ) P(RNS) A. 1/16 •B. None of thesev C. 0.87 D. 3/8 E. 0.36 The…
A: Solution: The fair coin is tossed three times the sample space Ω is Ω={ HHH, HHT, HTH,…
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- In a certain region, the probability of selecting an adult over 40 years of age with a certain disease is 0.05. If the probability of correctly diagnosing a person with this disease as having the disease is 0.86 and the probability of incorrectly diagnosing a person without the disease as having the disease is 0.06, what is the probability that an adult over 40 years of age is diagnosed with the disease? The probability is (Type an integer or a decimal. Do not round.)2. Iron bars produced by a machine can either be classified as "Good" with probability p, or "Bad" with probability q = 1- p. The quality of each iron bar produced is independent of each other. (a) Suppose there are n iron bars produced by the machine. Write down the probability that there are exactly r "Good" iron bars among the n of them for all positive integers r. (b) Suppose the machine keeps producing iron bars until k "Good" ones are obtained. Let X be the total number of iron bars produced. Show that the probability mass function of X is given by Px(x) = (x − 1) ₁² (1 - p)² -*. x=k, k +1,.... (c) In a single day, the machine produces exactly N = n iron bars, where N has mean and variance given by E(N) = a, Var(N) = 3. Let W be the total number of "Good" iron bars produced in a single day. i. Find E(W) and Var(W) in terms of p, a and 3. You can use the mean and variance of any standard distributions without proof as long as you state them clearly. ii. Determine the covariance…i need in words not handwritten
- Please I want a handwritten solution, not printedthere are no pairs of consecutive integers in the winning combination (i1,..., ix) if and only if (j1, ..., jk) has no repeats. The total number of winning combinations is In part k (c), we computed the number of winning combinations with no repeats among (j1,.. ,jk) to be n – k+1 So, the probability of no consecutive integers is k2. A number U is selected at random between 0 and 1. Let the events A and B be "U differs from 1/2 by more than 1/4" and "1-U is less than 1/2", respectively. Find the events An B, Ān B, AU B.
- 5.3 A bent coin, with heads probability .2, is tossed 13 times. Let X be the number of heads in the 13 tosses. Find (a) P(X =5), and (b) P(X = 12).B to A Use the probabilities in the first tree diagram below to find the probability of each branch of the second tree diagram to the right. A .B Start to B B to A' A" 1 Start B B' to A A Start to B' B' B" B' to A A" Start B B" Calculate each probability in the tree diagram. B to A= Start to B = B to A' = B' to A = Start to B' = B' to A' = (Type integers or simplified fractions.) - |en en |00 en IThe graph of the discrete probability to the right represents the number of live births by a mother 49 to 53 years old who had a live birth in 2015. Complete parts (a) through (d) below. 0 1 (a) What is the probability that a randomly selected 49- to 53-year-old mother who had a live birth in 2015 has had her fourth live birth in that year? (Type an integer or a decimal.) (b) What is the probability that a randomly selected 49- to 53-year-old mother who had a live birth in 2015 has had her fourth or fifth live birth in that year? (Type an integer or a decimal.) (c) What is the probability that a randomly selected 49- to 53-year-old mother who had a live birth in 2015 has had her sixth or more live birth in that year? (Type an integer or a decimal.) Statcrunch no JL @ 1 # с $ % JI JU & 0.30 0.25 0.20 0.15 0.10 0.05- 0.00 U 165 0.112 0.094 Number of Live Births 7 R # 8 A G
