Toss five fair coins and let x equal the number of heads...

Toss five fair coins and let x equal the number of heads observed. a. Identify the sample points associated with this experiment, and assign a value of x to each sample point. Then list all the possible values of x. b. Calculate p(x) for the values x = 1 and x = 4. c. Construct a probability histogram for p(x). d. What is P(x = 1 or x = 5)? a. What are the possible values of x? A. x = 1, 2, 3, 4 B. x = 0, 1, 2, 3, 4 C. x = 1, 2, 3, 4, 5 D. x = 0, 1, 2, 3, 4, 5 b. Calculate p(x) for x = 1. p(1) = (Simplify your answer.)

Transcript

00:01 So let's go ahead and answer these questions.

00:04 If we toss a fair coin five times, what is all these sample points that we can have? and let's assign a value of x to each sample point.

00:20 So let's go ahead and list all the sample points.

00:23 We would have two to the fifth because we have two different possibilities.

00:29 We have heads or tails.

00:31 And we're flipping this coin five times, hence the to the fifth part.

00:38 So we have two to the fifth with each is 32 different possibilities.

00:45 So we have heads, heads, heads, heads, heads.

00:50 We also have heads, heads, heads, tails.

00:56 Also, we have heads, heads, heads, tails heads.

01:00 And i'll go ahead and list all of them right now.

01:09 So first, in part a, we have to identify the sample points of the experiment here, in which we're flipping a coin, which has two total possibilities five times, so we take two to the fifth, and we get 32 total sample points.

01:30 Now, if we want to list them all, one of them could be, what if we get all heads? well heads heads heads heads heads what if we get four heads in the row then tails what if we get how about we get three heads in the rows then tails and then two more heads and we do this for each possible combination available so i will go ahead and do that right now so these are all of the possibilities of flipping a coin 32 times and getting different outcomes.

02:19 So that's for part a.

02:22 In part b, we're asked to calculate the probabilities of 1 and 4.

02:32 And this is x is the possibilities, or x is the number of heads.

02:39 So first, in a case where we have zero heads, all tails, that is a probability of 1 out of the total amount of probability is 32.

02:54 The possibility of having one head, we just look at all of these different probabilities.

03:00 Find the ones with only one head.

03:03 I could find a couple just for example.

03:05 One here, one here, one here...

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