A small deck of 8 cards consists of 5 red cards and 3 green...

A small deck of 8 cards consists of 5 red cards and 3 green cards. Draw one card at random. Let X = 1 If the card is red Let X = 0 if the card is not red Find the standard deviation of X. Round to three decimal places.

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Transcript

00:01 We have a set of 10 cards.

00:03 Three of them are red, seven of them are black.

00:05 We put them down and we start turning them over one at a time until we get to the first red card.

00:11 And we want to know the distribution of x, the number of cards we have to turn over.

00:22 Okay, is x a normal distribution with mean three, a binomial distribution, the geometric distribution, uniform, or none of the above? so let's go through some of the requirements here, when you would see these.

00:40 First of the normal.

00:41 First of all, this cannot be normal.

00:43 The normal distribution is continuous.

00:46 It can take any value.

00:48 X is discrete.

00:49 It can only take whole numbers.

00:51 It's either going to be one, two, three, up to ten.

00:55 If it take, well, not ten, really.

00:57 There's three red cards.

00:58 But it has to take whole numbers.

01:01 So it can't possibly be normal.

01:03 Besides, the normal distribution looks like this.

01:07 It's symmetric, it's unimodal, you see it for things where you have lots of tiny factors influencing something, like height or weight, or sample distributions.

01:19 B, a binomial.

01:20 So a binomial has a fixed number of independent trials, and you're looking at the number of successes...

Question

A small deck of 8 cards consists of 5 red cards and 3 green cards. Draw one card at random. Let X = 1 If the card is red Let X = 0 if the card is not red Find the standard deviation of X. Round to three decimal places.

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