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 06:45 PM.
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.