anybody?
1. A single die is rolled. Find the probabilities of the given events. (Enter exact numbers as integers, fractions, or decimals.) (a) rolling a 6
(b) rolling a 6, given that the number rolled is even
(c) rolling a 6, given that the number rolled is odd
(d) rolling an even number, given that a 6 was rolled
2. You order thirteen burritos to go from a Mexican restaurant, five with hot peppers and eight without. However, the restaurant forgot to label them. If you pick four burritos at random, find the probability of the given event. (Round your answer to three decimal places.) All have hot peppers.
3.You order seventeen burritos to go from a Mexican restaurant, nine with hot peppers and eight without. However, the restaurant forgot to label them. If you pick three burritos at random, find the probability of the given event. (Round your answer to three decimal places.) At most two have hot peppers.
4.Determine a casino's expected net income from a 24-hour period at a single roulette table if the casino's total overhead for the table is $30 per hour and if customers place a total of $5,000 on single-number bets, $4,000 on two-number bets, $4,000 on four-number bets, $2,000 on six-number bets, $7,000 on low-number bets, and $8,000 on red-number bets. (Assume the expected value of each of these $1 bets in roulette is −$0.053.
Last edited by RedGuard; April 19, 2015 at 07:45 PM.
1.a. Since you have a single six-sided die, there is one favorable outcome (1) out of six possible outcomes (6) - 1, 2, 3, 4, 5, and 6. So the probability is 1/6.
1.b. You know the dice rolled an even number, so that leaves us with the only even numbers on the die: 2, 4, and 6. Six is the only favorable outcome, with three possible ones, so the probability is 1/3.
1.c. 0, six isn't odd.
1.d. 1, six is even.
2. If you select one burrito, five of the thirteen have hot peppers (5/13) and eight of the thirteen don't (8/13, and 5/13 + 8/13 = 1), so if you remove a burrito, it's a 5/13 probability it has hot peppers. Now there are only twelve burritos left, four with hot sauce, etc. Since you take four burritos out and remove them from the group of possible outcomes, the equation is 5/13 * 4/12 * 3/11 * 2/10 = 1/143, or ~0.007, or ~0.7%.
3. These better be great burritos, because this restaurant has terrible service. Here is an extremely drawn-out, brute force method to do it - which I don't recommend but it's to show what's being done. So if h = burrito with hot peppers and n = burrito without hot peppers, the successful combinations are hhn, hnh, nhh, hnn, nhn, nnh, and nnn. The probability of any of these events occurring is:
P(hhn V hnh V nhh V hnn V nhn V nnh V nnn)
P(hhn) + P(hnh) + P(nhh) + P(hnn) + P(nhn) + P(nnh) + P(nnn)
P(9/17 * 8/16 * 8/15) + P(9/17 * 8/16 * 8/15) + P(8/17 * 9/16 * 8/15) + P(9/17 * 8/16 * 7/15) + P(8/17 * 9/16 * 7/15) + P(8/17 * 7/16 * 9/15) + P(8/17 * 7/16 + 6/15)
576/4080 + 576/4080 + 576/4080 + 504/4080 + 504/576 + 504/4080 + 336/4080
= 3576/4080 = ~0.876, or 87.6%
4. I've never played roulette, so I don't know the terminology. Sorry.
Now that we know this is your math homework and you're not asking us to help feed a gambling addiction, I feel the need to point out that if you cannot solve at least most of these, you are going to be in trouble. You have to know this level of stuff to pass math on the high school level. If you simply don't get it on the conceptual level, see if your school has some kind of tutoring outside of class or explain your confusion to the teacher. I think that's the best way.
Last edited by pacifism; April 21, 2015 at 06:06 PM. Reason: I messed up
Stupid truth: always resisting simplicity.
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Looking back, I think I would find me-from-the-past to be an insufferable idiot if I ever had the displeasure of meeting him.
thanks for the answers. lol, no its not a gambling addiction. I am taking the easiest math class in college that I can take because I am terrible at math. I currently have a B+ in this class, but the thing is I don't remember learning probabilities and odds in highschool, but I think I'm getting the hang of it now. I should have taken a real class and not an online one, because I can't really ask people questions so I come here. Thanks for answering and putting up with my questions. you and the people here have actually explained it much better to me than the piece of crap book I had to buy for 70 dollars. From now on If I ask a question it will be because I exhausted all other possibilities.
I doubt anyone would pose that as a problem, as the result is not analytically presentable. You can just rewrite the integral and numerically solve it if boundaries are given.
"Non i titoli illustrano gli uomini, ma gli uomini i titoli." - Niccolo Machiavelli, Discorsi
Under the patronage of the impeccable Aikanár, alongside Neadal, Squeaks, Makrell, Kaiser Leonidas, Sheridan, Bercor and Higo Chumbo. Humble patron of Cyclops, Frunk and Abdülmecid I.
On an eternal crusade for reason, logics, catholicism and chocolate. Mostly chocolate, though.
Heh I guess there's this:
https://math.stackexchange.com/quest...-sqrt-sin-x-dx
I didn't study elliptic integrals myself, just figured it would be a composition.
Composite functions are usually integrated by clever substitution + a varied assortment of minor tricks in manipulating terms. The one in question does not have an analytic solution, though. The elliptic integral function involved in presenting the indefinite integral of sqrt(sin x) is itself only defined as the integral of a certain function where the variable is placed as one of the bounds.
"Non i titoli illustrano gli uomini, ma gli uomini i titoli." - Niccolo Machiavelli, Discorsi
Under the patronage of the impeccable Aikanár, alongside Neadal, Squeaks, Makrell, Kaiser Leonidas, Sheridan, Bercor and Higo Chumbo. Humble patron of Cyclops, Frunk and Abdülmecid I.
On an eternal crusade for reason, logics, catholicism and chocolate. Mostly chocolate, though.
Ugh, I'm struggling with this statistics set. I'm looking over budget projections and I'm having a difficulty.
So a budget projection shows us at a $6.1 million fund balance for this year, this was asserted with a 95% certainty. The actual outcome was a $7.4 million fund balance. Meaning somehow we under-projected revenues+over-projected costs by 1.3 million.
Is there a way to calculate the likeliness of this outcome given our earlier projection? I feel like I need more data but I'm struggling to figure out what it is and it's been far too long since I've done statistics.
"Pride is not the antidote of Shame but its source, humility is its only true antidote." - Iroh
Not sure if what you need is statistical sophistication or perhaps the margin of error is already part of your data? One approach I've seen to forecasting algorithms is to calculate your historical margin of error - given an algorithm and a history of a few years, calculate what the forecast was and how far off the subsequent results were. That tells you at least historically how far off your predictions have been.
I think Iskar may have better mathematical suggestions