3:10, I didn't subtract 5 from prize before calculating the gross income and only subtracted 5 from the final result and I got the same number this way. I think that's handier, since we only need to subtract 5 once and we even get the gross income.

@varun0904

4 ай бұрын

You can see why you get the same answer by writing the expected profit as = Prob(Grand prize)*(Grand prize - ticket) + Prob(small prize)*(small prize - ticket) + Prob(No prize)*(0 - ticket) = Prob(GP)*(GP) + Prob(SP)*(SP) + Prob(NP)*(0) - ticket*[Prob(GP) + Prob(SP) + Prob(NP)] Now that factor multiplying the ticket cost is just 1 because that's is the probability of ANY event happening - giving you the same answer :)

actually to be fair, it would make sense to buy every ticket. that would mean you would have to spend $13000 on 2600 total tickets, in which you would for sure get the grand price of 10405. also, you would get 99 small prizes cause 99 other tickets have a matching letter but incorrect numbers, so that would mean u made a total of $20305 on a $13000 investment. its a much smarter move than going off to college and drowning in debt and possibly pussy.

@azadkaya

7 жыл бұрын

liverpooler1997 how do you know there is a total of 2600 tickets?

@xybersurfer

6 жыл бұрын

Azad Kaya it says he gets to pick 2 numbers 0-9: 100 possibilities it also says he gets a letter: 26 possibilities 100 * 26 = 2600 possibilities

Hi! Thanks for the explanation. Note that alternatively the expectation can be calculated without subtracting the prices with the participation cost: 1/2600*10405+(1/26-1/2600)*100-5

@wxplorer3343

4 жыл бұрын

Tessa van der Heiden Can you explain the probability P(small)? I am confused about subtracting P(grand) from 1/26

@warpiwarpi3533

4 жыл бұрын

I also did like that, much easier :)

@OrenLikes

2 жыл бұрын

@@wxplorer3343 10405*(1/26)*(1/100)+ 100*(1/26)*(99/100)+ 0*(25/26)*(100/100)- 5 would make more sense... 10405 for one letter out of 26 and 1 two-digit combination out of 100, plus 100 for one letter out of 26 and any other two-digit combination of of 100, which is 99 out of 100, plus 0 for any other letter, which is 25 out of 26 and any two-digit combination out of 100, which is 100 out of 100, minus 5 the cost of the ticket. and simpler: less calculation regarding cost of ticket -> deferred to the end.

For winning the small prize, you can think of it as follows : There are three places : _ _ _ He can get each place as Right (R) or Wrong (W). Since we are calculating the case where the letter is always right, lets fix that position: _ _ R Case 1 : He gets the first digit right - R W R : 1/10 . 9/10 . 1/26 (Since getting a wrong digit is nothing but 1- getting a right digit) Case 2 : He get the second digit right - W R R : 9/10 . 1/10 . 1/26 Case 3 : He gets both digits wrong - W W R : 9/10 . 9/10 . 1/26 Adding the three cases we get : 9/2600 + 9/2600 + 81/2600 = 99/2600 This is same as saying 1/26 - 1/2600

@rikawrites7104

9 ай бұрын

i have done the problem this way too !! thanks :)

@Sal Doesn't the final answer apply to just the "Frequentist view of probability"? i.e. If I play many many times, then at the end of the day I'll have 2$ more in my wallet than when I started. But, if I think in terms of chance (Bayesian view), i.e. if I get to play the game just once (meaning you are not allowed to draw multiple tickets), then there's no way that I'll ever get 2$; I'll either win or lose. So the expected value we got won't make sense then, right?

@lvlycreator92

3 жыл бұрын

This is exactly what I was thinking too. Because the problem clearly states that 04R is the ticket drawn which means Ahmed is not going to draw multiple times. so the possible net profits would be 10,400$ or 95$ or nothing. It is not possible to get a net profit of 2$ in this case right?.

@durgaprasadsamantula699

3 жыл бұрын

@@lvlycreator92 I am also thinking the same !!!

TTThanks

This teacher uses a method that I can understand. How do I find statistic videos from him specifically?

@shekelboi

5 ай бұрын

Just Google Khan Academy AP Statistics and you'll see a bunch of statistics videos + exercises from him.

With enough patience and money - "Winner, winner chicken dinner."

or we can also do 1/26*9/10*9/10 for the 95$ net profit case

10405*(1/26)*(1/100)+ 100*(1/26)*(99/100)+ 0*(25/26)*(100/100)- 5 would make more sense... 10405 for one letter out of 26 and 1 two-digit combination out of 100, plus 100 for one letter out of 26 and any other two-digit combination of of 100, which is 99 out of 100, plus 0 for any other letter, which is 25 out of 26 and any two-digit combination out of 100, which is 100 out of 100, minus 5 the cost of the ticket. and simpler: less calculation regarding cost of ticket -> deferred to the end.

Can someone clarify the probability for winning small price please. How P(small) = 1/26-(1/2600) ? Since 1/2600 also includes the probability of picking correct alphabet that should n't be subtracted, i believe. Am I missing something here ?

@wxplorer3343

4 жыл бұрын

Stalin Amirtharaj +1

@OrenLikes

2 жыл бұрын

10405*(1/26)*(1/100)+ 100*(1/26)*(99/100)+ 0*(25/26)*(100/100)- 5 would make more sense... 10405 for one letter out of 26 and 1 two-digit combination out of 100, plus 100 for one letter out of 26 and any other two-digit combination of of 100, which is 99 out of 100, plus 0 for any other letter, which is 25 out of 26 and any two-digit combination out of 100, which is 100 out of 100, minus 5 the cost of the ticket. and simpler: less calculation regarding cost of ticket -> deferred to the end.

I solved the question the same way and got 3.0 dollars. Can someone explain to me what went wrong. I want to know if it was an approximation error on their part or mistake on mine

At 4:34, I calculated P(small) differently. First, we get the probability of selecting only the correct letter. That is 1 over 26. Second, the question said "but one or both of his numbers do not match." This means he didn't select the correct number. If he did, he would've won the grand prize. Now, how many correct numbers in the pool of 100 numbers (e.g. 22, 90, 09, 18, 65)? One! How many incorrect numbers are in the pool? 99! Let's remove the correct number, so we end up with a pool of 99 incorrect numbers. Now, what is the probability that we select an incorrect number? It's 1 over 99. Multiply 1 over 26 by 1 over 99. The result is equal to 1/26 - 1/2600!

Haha Description is 'Description' and Add a Message is ' Add a Message'. good thing the video name isn't 'video Name'!

bro they could've made the digital calculator cleaner

conclusion: buy one of every possible combination for a $7000+ profit

@kyh6767

6 жыл бұрын

unless one can win once only

Why P(grand) is 1/10 . 1/10 . 1/26 and not 1/10 . 1/9 . 1/26?

@mustavogaia2655

5 жыл бұрын

both draws include the 10 numbers.

@wxplorer3343

4 жыл бұрын

The problem says that you can choose the same number second time which means that the numbers are chosen with replacement.

Error in Sal's explanation? At 6:26 he simplifies a problem {1-(1/26 MINUS 1/2600)-1/2600} into {1-1/26 PLUS 1/2600-1/2600}. Someone please take me to school on this and tell me how that is possible? With addition and subtraction, parentheses shouldn't be able to change the +ve or -ve of the number.

@bbeaum1

10 жыл бұрын

Sallable the infallable. I got it now. Scratched it out on some paper with some different number examples. I'm a French major that is re-learning math. Excuse the ignorance. Parentheses do change the +ve and -ve. Snap!

yyyyyeeeeaaaahhh 3rd to post baby!