If A and B are events such that P(A) = 0.5 and P(AUB) = 0.7, find P(B) when (a) A and B are disjoint; (b) A and B are independent. (a) If A and B are disjoint events, then P(B) = (Type an integer or a decimal.) (b) If A and B are independent events, then P(B) = (Type an integer or a decimal. )Complete the tree below and find Pr( B|D). C A .4 D .2 C .3 B D 5 EWhich of the following are steps for solving Bayesian probability problems from this section? Select all that apply. Use the tree diagram to answer the two pieces of the conditional formula. Convert all probabilities on the tree diagram to odds. Use the conditional probability formula. Make sure that the events in the experiment are independent. Construct a tree diagram. Write the question as a conditional. Which of the following are true about an experiment consis- of a sequence of Bernoulli trials? Select all that apply. [I Each individual trial can result in only two possible outcomes: "success" or "failure." 3 The probability of success (p) changes with each trial. :| The trials of the experiment must be dependent. :l The probability of success (p) is the same for each trial. :| The trials of the experiment must be independent. :| There must be multiple trials to the experiment. Given a sequence of Bernoulli trials with n = 7, k is at least 1, and p = 0.35, find the binomial probability. O 0.9510 O 0.0006 O 0.0490 O 0.8152 O 0.9994 O 0.1848An unfair coin with 0.6 probability of tails is ipped 11 times. What is the probability of obtaining exactly ve tails? Without calculating the answer, what are the values of n, k, p, and q that would be required to solve this problem using the binomial probability formula C (n, k) -pk - qnk ? The value of n in this problem is [Choose] The value of k in this problem is [Choose] The value of p in this problem is [Choose] The value of q in this problem is [Choose] A fair die is thrown 20 times. What is the probability of getting the point \"5\" on exactly seven of the 20 rolls? It is found that 7% of watches produced at a particular factory are defective. If 16 watches made at this factory are randomly selected, what is the probability that at most 1 watch in the sample is found to be defective? 0 0.6229 0 0.3131 0 0.6869 0 0.3098 0 0.3771 0.6902 D. 0.7 M MT 0.1 T 0.4 0.2 0.1 NW T 0.2 M 0.5 0.3 T NW 0.5 NWB. 0.2 Worn Fiction 0.3 0.8 Good 0.2 Worn 0.7 Nonfiction 0.8 GoodCompute the G.P.A for the students whose grades are shown in the table below. Letter Grade Value Frequency A 4 28 B 3 58 C N 19 D 5 C 4\fA random variable X has the probability density function below. Find the standard deviation of the random variable. X Pr(x) X . Pr (X) X - ul ( X - M) 2 (X - M)2 . Pr(X) (2) 0 0.3 0.6 4 0.1An unfair coin with Pr(H) = 0.54 is flipped 300 times. A random variable X is defined as the number of heads that occur. Find the u and o. (2) O=_ (2)