1)a) P(a) =P(A)-P(C)=1/2-10/21 =1/42
P(d) =P(S)-P(A)=1-1/2 =1/2
b)here P(C)*P(A)=1/3........(1)
P(A)-P(C')=P(A)-(1-P(C))=P(A)+P(C)-1=1/3
P(A)+P(C)=4/3 .......(2)
solving equation (1) and (2)
P(A)=1
and P(C)=1/3
therefore
P(a) =P(A)-P(C)=1-1/3 =2/3
P(d) =P(S)-P(A)=1-1 =0
1. Let S P(ta), P(ld) if you are given that {a,b,c,d) be a sample space and...
Let S = {a,b,c,d) be a sample space and A = {a,b,c}, B = {a,b,d) and C = {b, c). P(a), P(d) if you are given that 1. Calculate the probabilities a) P(A) = , P(B) = and P(C) = b) P(C)P(A)- P(A) - P(C).
Let and B be events in a sample space S, and let C = S - (AUB). Suppose P(A) = 0.8, P(B) = 0.2, and P(An B) = 0.1. Find each of the following. (a) P(AUB) (b) P(C) (c) PAS (d) PLAC BC) (e) PLACUBS (1) P(BCnc)
A random experiment has sample space S={a, b, c, d}S={a, b, c, d}. Suppose that P({a, d})=38, P({a, b})=58P({a, d})=38, P({a, b})=58, and P({d})=18P({d})=18. Use the axioms of probability to find the probabilities of each of the elementary events.
[15] 4. Let E and F be events of sample space S. Let P(E) = 0.3, P(F) = 0.6 and the P(EUF) = 0.7. a) Fill in all probabilities in the Venn diagram shown. S b) Find P(EnF). c) Find P(ENF). d) Find the P(E|F). e) Are E and F independent events? Justify your answer.
Q2. 5 marks] The sample space of a random experiment is (a; b; c; d; e) with probabilities 0.1, 0.2, 0.2, 0.1, and 0.4 respectively. Let A denote the event fa; b; c) and let B denote the event (b; c; e a. Determine P(A | B') b. Are the events A and B independent?
3. Let A, B, C be events in a sample space S. Prove that (a) P(AUB) P(A)P(B), (b) P(AUBUC) P(A)+P(B)+P(C)-P(AnB)-P(Anc)-P(Bnc)+P(AnBnc)
C. Let S represent the sample space of classrooms on C classroom without a projector i. Compute the probability P(A nBnC). campus. Events are defined as follows: A classroom remodeled/built within the last 5 years B- classroom with a window(s) The following probabilities are known: PCA)0.1, P(B)0.6, P(C)0.3, P(An B)0.1, P(AnC)- 0.0, and P(B nC)0.2 ii. Compute the probability P(A UBUC) ii. Provide evidence, using the rules of probability, that you cannot find a classroom remodeled/built within the last 5...
C. Let S represent the sample space of classrooms on C classroom without a projector i. Compute the probability P(A nBnC). campus. Events are defined as follows: A classroom remodeled/built within the last 5 years B- classroom with a window(s) The following probabilities are known: PCA)0.1, P(B)0.6, P(C)0.3, P(An B)0.1, P(AnC)- 0.0, and P(B nC)0.2 ii. Compute the probability P(A UBUC) ii. Provide evidence, using the rules of probability, that you cannot find a classroom remodeled/built within the last 5...
Let A and B be events in a sample space S such that P(A) = 0.33, P(B) = 0.35 and P(A ∩ B) = 0.14. Find P(A | B).
2. Let A and B be subsets of a sample space S. The relative complement of B with respect to A is denoted and give by A B(r:r E A and r (a) Express B as a relative complement. (b) Prove that A B An B. (c) Prove that (A\B) A*UB. (d) Prove that p(AP)-P(1)-P(An B). B).