2. You plan to toss a possibly biased coin (with probability...

2. You plan to toss a possibly biased coin (with probability $p$ getting a head and probability $1 - p$ getting a tail) 100 times. If you get a head for the 100th toss, you will keep tossing the coin until you get a tail. (a) Find the expected number of tosses that you make. (b) Find the expected number of tails that you observe.

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00:01 A coin is biased so that it has a 60 % chance of landing on heads.

00:04 You toss the coin three times.

00:08 So we have heads tails, heads tails, and the third toss, heads tails again.

00:24 A success is any time the coin lands on tails.

00:27 Create a tree diagram, which is what we just did, and then list the following the outcomes and the probability of successes.

00:34 And then we're going to answer some probability questions.

00:37 So again, remember that heads is 0 .6.

00:45 Which means that getting a tails is .4.

00:57 So when we look at our outcomes, we could have heads, heads, heads, heads, heads, heads, heads, heads, heads, heads, heads, tails, tails, heads, heads, heads, tails, tails, tails, tails, heads, and tails, tails, tails.

01:18 And calculating the probabilities for those, heads, heads, heads, heads would be 0 .6 to the third power.

01:24 Heads, heads tails would be 0 .6 squared times 0 .4.

01:29 And we have that a few times.

01:31 So 0 .6 squared times 0 .4.

01:34 Here's another one.

01:35 0 .6 squared times 0 .4.

01:39 When we have two tails, it'll be 0 .6 times 0 .4 squared.

01:42 And again, we have that.

01:44 0 .6 times .4 squared, three times...

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