please help!

[jelly1213]

1.Five policemen and five thieves stand in a line for a picture. What is the probability that all the policemen stand together while the thieves DO NOT ALL stand together? Answer should be a common fraction.
2. An unfair coin shows heads 2/3 of the time. What is the probability that it shows heads exactly five out of seven flips? Answer should be a common fraction.
3.Ricky has a dumpling five-shooter with one dumpling in one of the five chambers. He spins it and fires, repeating this two-step process until he gets the dumpling to come out. What is the probability that he gets the dumpling to come out on the 2nd or 4th shot? Answer should be a common fraction

 

[Dr.Peterson]

1.Five policemen and five thieves stand in a line for a picture. What is the probability that all the policemen stand together while the thieves DO NOT ALL stand together? Answer should be a common fraction.
2. An unfair coin shows heads 2/3 of the time. What is the probability that it shows heads exactly five out of seven flips? Answer should be a common fraction.
3.Ricky has a dumpling five-shooter with one dumpling in one of the five chambers. He spins it and fires, repeating this two-step process until he gets the dumpling to come out. What is the probability that he gets the dumpling to come out on the 2nd or 4th shot? Answer should be a common fraction

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1. Apparently you are to assume that all arrangements in a single line are equally likely. You need PPPPP with T's on either side, but not PPPPPTTTTT or TTTTTPPPPP. How many ways can you do that?

2. Have you learned about the binomial distribution? If not, you will be inventing it.

3. You want the probability of getting either XD or XXXD.

What have you tried?

 

[jelly1213]

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Welcome to our tutoring boards! :) This page summarizes main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to help...

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1. Apparently you are to assume that all arrangements in a single line are equally likely. You need PPPPP with T's on either side, but not PPPPPTTTTT or TTTTTPPPPP. How many ways can you do that?

2. Have you learned about the binomial distribution? If not, you will be inventing it.

3. You want the probability of getting either XD or XXXD.

What have you tried?

i have figured out the first 2, but need help starting the third. I know that The probability of the dumpling being shot out on the first try is 1/5. The probability of it being shot out on the second try is 1/4 because there are only 4 places where the dumpling can be shot out of. The third is 1/3. The fourth is 1/2. The fifth is 1 because it is the only place where the dumpling can be shot out of. I am confused on how to calculate getting shot out from the 2nd or 4th time?

 

[Dr.Peterson]

i have figured out the first 2, but need help starting the third. I know that The probability of the dumpling being shot out on the first try is 1/5. The probability of it being shot out on the second try is 1/4 because there are only 4 places where the dumpling can be shot out of. The third is 1/3. The fourth is 1/2. The fifth is 1 because it is the only place where the dumpling can be shot out of. I am confused on how to calculate getting shot out from the 2nd or 4th time?

You seem to be thinking of a different problem, in which each each chamber can only be tried once. That isn't what it says:

3.Ricky has a dumpling five-shooter with one dumpling in one of the five chambers. He spins it and fires, repeating this two-step process until he gets the dumpling to come out. What is the probability that he gets the dumpling to come out on the 2nd or 4th shot? Answer should be a common fraction

The probability of the dumpling coming out on any given shot, IF it hasn't come out yet, is always 1/5, because there is one chamber containing the dumpling, and each spin is independent, equally likely to bring the dumpling into position. (If is has already been shot, the probability changes to 0.)

You're forgiven if you don't quite picture a dumpling five-shooter quite right; I've never seen one either!

Now, try again: You want the probability that it doesn't come out on the first, but does come out on the second; and then the probability that it doesn't come out on the first, second, or third, but does on the fourth.