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An experiment consists of two independent trials. The outcomes of the first trial are A, B, and C, with probabilities of occurring equal to 0.2, 0.4, and 0.4, respectively. The outcomes of the second trial are E and F, with probabilities of occurring equal to 0.7 and 0.3. Draw a tree diagram representing this experiment. Use this tree diagram to find the probabilities below.  (a)    P(B)(b)    P(F | B)(c)    P(B  F)(d)    P(F)(e) Does P(B  F) = P(B) · P(F)? YesNo     (f) Are B and F independent events? YesNo

need assistance with cylinridical coodinates for laplace eqn PDE

Given P(A) = 0.10, P(B) = 0.08, and P(A or B) = 0.18, are events A and B mutually exclusive?

The table below shows the probability of winning 0-5 dollars playing a game.   Amount Won ($) 0 1 2 3 4 5 Probability 4/24 7/24 7/24 3/24 2/24 1/24   The stallholder charges $2.50 for each playing of the game. How much money can the stallholder expect to make for the charity on a day when there are 400 plays of the game?

Rodney is going to shoot a total of 9 free-throws to prove he is a better shooter than Chris. During warm-ups Rodney can make 57% of practice shots. The challenge results are as follows… • 9 hits Rodney wins $100 • 6-8 hits Rodney wins $25 • 4-5 No one wins • 0-3 hits Chris wins $15 What is the probability that Rodney makes 7 shot?

P(A)=0.55,P(B)=0.58,P(B∪A)=0.86 Find the following probabilities. P(A∩B) =  P(B|A) =  P(A|B) =