Rework problem 17 from section 33 of your text involving...

Rework problem 17 from section 3.3 of your text, involving filling in missing probabilities on a tree diagram. Construct a copy of figure 3.10 in your text, where the first outcome is one of (A, B, C) and the second outcome in each case is one of (1, 2). Use the following probabilities instead of those given in your text: Pr[A] = 1/16 Pr[A1] = 1/24 Pr[A2] = 1/8 Pr[1|B] = 1/2 Pr[2|B] = 1/2 Pr[B1] = 1/4 Pr[B2] = 1/4 Pr[C1] = 1/4 Pr[C2] = 1/12 Find the following missing probabilities: (1) Pr[1|A] = (2) Pr[B] = (3) Pr[C] = (4) Pr[2|C] =

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00:01 Okay, so to start this problem off, we're making a tree diagram where the first outcome is one of a or b or c.

00:09 And then the second outcome in each case is one of one or two.

00:13 Okay, so each of these have a one and a two for our tree diagram.

00:19 And we are told a few probabilities.

00:21 We're told the probability of a is 1 out of 16.

00:27 The probability of a then a worm is 1 out of 24, so that's at the end of this, right? this is 1 out of 24.

00:40 The probability of a2 is 1 out of 8.

00:44 Probability of 1 given b is 1⁄2, so that would be right here, right? one half.

00:56 Probably of two given b is also one half.

01:01 Probability of b1 is one -fourth.

01:06 Sorry, there should be an arrow right there.

01:12 Okay.

01:13 The probability of b2 is one -fourth.

01:21 Probability of c -1 is one -fourth.

01:26 Probability of c -2 is 112 and so we are supposed to find the following probabilities we're supposed to find the probability of one given a the probability of b the probability of c and the probability of two given c so the probability of one given a is going to be this area right here the probability of b is going to be this area here here, the probability of c is going to be this area right there, and the probability of two given c is right there...

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