1 explain what each of the following probability values...

1. Explain what each of the following probability values implies about the likelihood of event A occurring. a) P(A) = 1 b) P(A) = 0 c) P(A) = 0.5 2. What is the probability of drawing each of the following from a standard deck of cards? a) a red card b) a club c) a 6 d) a face card e) a black ace 3. A couple plans to have three children. Construct a tree diagram to illustrate the possible gender outcomes of the three children. 4. Refer to question 3. What is the probability that the couple will have a) three girls? b) two boys? c) not all girls? d) a girl, then a boy, then a girl? e) State any assumptions you must make in your calculations. 5. A coin is flipped ten times, and turns up heads six times. a) Based on these results, what is the empirical probability of flipping heads with this coin? b) Can you conclude that this coin is unfair? Explain. c) Explain how you can draw a better conclusion regarding the fairness of this coin. 6. Estimate subjective probabilities for each of the following events. a) It will snow tomorrow. b) The next school bell will ring on time. c) USA will win at least one gold medal in the next Olympic Games. d) The price of gas will rise at least once in the next week. 7. For each of your estimates in question 6, provide a rationale for your answer. 8. What is the probability of not rolling an 11 with a standard pair of dice? 9. For what probability will an event be twice as likely to occur than not occur?

Transcript

00:01 For your first question, we want to explain what each of the following probability values implies.

00:08 And part a is the probability that a equals 1.

00:14 That is what we would reference as a certain event, which means that event a will definitely occur.

00:35 For part b, we want the probability of a equals zero, and that is defining the probability that event a will never occur.

00:53 It will not happen.

00:55 And then in part c, the probability of a is equal to 0 .5 means that there is just as likely a chance that event a will happen or will not happen.

01:29 So the likelihood of it happening is the same as the likelihood of it not happening.

01:40 So for problem number two, we're dealing with a standard deck of cards.

01:46 So therefore you need to know that in a standard deck of cards, there are 52 cards.

01:52 There are four suits of cards.

01:57 There are diamonds.

02:01 Hearts, spades, and clubs.

02:11 There are 13 of each and they run from ace up through king.

02:22 So in part a, we want to determine the probability of a red card.

02:31 So there are 13 diamonds and 13 hearts, all of which are red.

02:37 So there are 26 out of the 52 or you have a probability of one half.

02:46 Part b is the probability that a randomly selected card is a club.

02:52 Well, there are 13 clubs out of 52 cards, which is a probability of one -fourth.

03:00 Part c is the probability of getting a six.

03:04 Well, there are four sixes in a standard deck of cards.

03:09 There's a six of diamonds, a six of hearts, a six of spades, and a six of clubs.

03:15 So there are four out of 52, which yields a probability of one out of 13.

03:22 In part d, we are looking for the probability of a face card.

03:30 And your face cards are your kings, queens, and jack.

03:37 And we have a king, queen, and jack of diamonds.

03:42 We have a king, queen, and jack of hearts.

03:46 We have a king, queen, and jack of clubs.

03:51 And we have a king, queen, and jack of spades.

03:58 So therefore, there are 12 face cards out of 52 cards, and 12 out of 52 would simplify down into 3 out of 13.

04:12 And for part e on this problem, the probability of a black ace.

04:20 Well, there's the ace of spades and the ace of clubs, so there are two out of 52 cards that would be classified as black aces, so that would be a probability of 1 out of 26.

04:33 For problem number three, we want to draw a tree diagram to illustrate the possible gender outcomes of having three children.

04:46 So the first child, you might have a boy or a girl.

04:51 Then the second child might be a boy or a girl.

04:56 And then the third child might be a boy or a girl.

05:01 So this is what your tree diagram would look.

05:05 Look like.

05:07 And now in problem number four, we want to use that tree diagram to find the various probabilities.

05:16 So before we do that, i want to construct our sample space.

05:20 Our sample space would be following each path.

05:26 So if we follow this path, then we have a boy, boy, and then boy.

05:31 If we follow this path, we get boy, boy, girl.

05:37 If we follow this path, we get boy, girl, boy.

05:43 And if we follow this path, we get boy, girl, girl.

05:48 If we follow this path, we get girl, boy, boy.

05:54 Following this path, we get girl, boy, girl.

05:58 Girl.

05:59 Following this path, we get girl, girl, boy.

06:04 And following the final path, we find girl, girl, girl.

06:10 So in part four, when it says, what's the probability of getting three girls? there's only one way that happens out of the eight in the sample space.

06:23 So it would be one out of eight.

06:25 For part b, we want the probability of two boys.

06:32 So there's a question that you might have to pose to your teacher, whether this means only two boys or there are two boys out of the family.

06:43 So we can do one of two things.

06:45 If it's only two boys, then this is only two boys, this is only two boys, and this is only two boys, so we could say three out of eight, but by them just saying two boys, that could mean that they have a third boy as well.

07:05 So therefore, if we throw that in the mix, it could be four out of eight or one half.

07:14 For part c, what's the probability of not all girls? the probability of not all girls.

07:27 Well, that means that this is not all girls.

07:32 This is not all girls.

07:34 This is not all girls.

07:36 This is not all girls.

07:38 This is not all girls.

07:39 This is not all girls.

07:41 And neither is this.

07:43 So it's going to end up being seven out of eight.

07:47 Another way you could have said it would be one minus the all girls, which would be one out of eight, which would also.

07:54 Get you that seven out of eighths.

07:58 And then part d, the probability of going in this specific order, a girl followed by a boy, followed by a girl, boy, girl, boy, there's only one way that happens...

Question

Please give Ace some feedback