Determine whether the following individual events are...

Determine whether the following individual events are independent or dependent. Then find the probability of the combined event. 1.) Drawing three jacks in a row from a standard deck of cards when the drawn card is not returned to the deck each time -The event of drawing a jack and the event of drawing a jack the next time are dependent or independent. -The probability of drawing three jacks in a row from a standard deck of cards when the drawn card is not returned to the deck each time is? 2.) Use the definitions given in the text to find both the odds for and the odds against the following event. -Flipping 4 fair coins and getting 0 heads. The odds for getting 0 heads are what to what.(Type a whole number.) The odds against getting 0 heads are what to what. (Type a whole number)

Transcript

00:01 So for part one, where we're drawing three jacks in a row without replacement, we are going to have that this is going to be a dependent event.

00:12 Or these are going to be dependent events.

00:15 If we say, for instance, j1 is a jack, the first card, say jack, and j2 is the event that the second card is a jack, and so on, the events j1, j2, and j3 are dependent.

00:35 Particularly because we'd have the probability of getting a jack as the second card, given that we got a jack as the first card, would be equal to, actually i'll start off with just the probability of j1, getting a jack when we have the full deck of cards.

00:52 There are four jacks overall, and there are 52 cards in the deck, so that's four out of 52.

00:57 The probability of getting a jack as the second card, given that we got a jack as the first card would be equal to 3 over 51.

01:09 Whereas if we got a jack as the second card, given that we did not get a jack as the first card, that would be 4 over 51.

01:17 So that's proof enough there that the events are dependent.

01:22 That being said, the probability of getting a jack as the first, jack as the second, and a jack as the third would be equal to 4 over 52 times 3 over 51 times now probability of getting a jack third when we've already removed 2 from the deck would be 2 over 50 and calculating that probability out i'm just going to do that off screen here that's going to come out to a probability of 0 .018 then for part for part 2 the second question let's see.

02:06 We have that odds 4 can be described as the reduced ratio of probability that a particularly outcome occurs, p, divided by 1 minus p.

02:21 So that's the probability that the outcome does not occur.

02:26 And then odds against, odds against, we can think of as just being the probability that we do not win.

02:41 Or the event does not occur, 1 minus p, divided by the probability that the event does occur.

02:49 So, divide by p...

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