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How many ways can person toss coin 13 times so that the number of tails Is between and ]] inclusive?...

Question

How many ways can person toss coin 13 times so that the number of tails Is between and ]] inclusive?

How many ways can person toss coin 13 times so that the number of tails Is between and ]] inclusive?



Answers

Use an appropriate rule of counting. If a fair coin is flipped three times, how many different sequences of heads and tails can be formed?

Okay, so we toss a coin 10 times, and we want to find how many different ways we can get heads and tails so our string of random heads entails. Well, it's something like, you know, and each, uh, for 10 it will be a 10 length string with, um, Agent t. So let's say we have 1234567 89 10. We have 10 positions for the outcomes of our coin. So in this first position, we can have either in HRT signifying head or tails. So we have two possible options for that. And for a second position, we can still get heads or tails were flipping another coin. That's gonna be another two possible options. For the third. It's gonna be the same thing. And for all of these will have two ways. We'll have two options of which way the outcome of our coin. And since we have 10 of these, it'll be two times two times 2 10 times or two to the 10th which is 10 24. So there are 1000 and 24 different 10 length combinations of flipping point

In this question, a coin is tossed three times and the outcomes are recorded. We are required to find the possible number of outcomes. So in the first coin doors, the possible outcomes are head or tails. Similarly, in the second and the third coin doses, the outcomes will again be head or take. Therefore, we can say that the total number of outcomes Will be to multiply with, to multiply with two, which will be equal to eight.

So this time we have four pennies and with three nickels have two dimes and 3/4. We're gonna put them in a row. So, total, we have five and seven, we have 12 over. And then we do our repetitions for factorial three factorial, two factorial and three factorial. And so I'm gonna take out the biggest one first. So that's gonna leave me with 12 11 10 9876 or so forth. Take out the four back Dorial. And then I have three times, Two times one times two times woman, sometimes three times to done for. So they're going to try to cancel some stuff out. Well, if I know, I know three times two is six times two is 12. So I could take the 12 out and three times two is six. I can take the six out. So now I could multiply what's left together 11 times, 10 times, nine times, eight times seven times Startup. I'm gonna get 277,000 200

So we want to find the probability of getting three tails. And that is if we toss a coin three times in a row now we can write the entire sample space out. And I did that on the previous question on this one, I'm not going to do that, I'm going to do a little bit different way. We can say well the first coin can come up any one of two ways. The second coin can come up any one of two ways and the third coin can come up any one of two ways. And so there are eight items in the sample space. If we write them down Now, how many of those ways will have exactly three tails? The the Tosses of tails tails tails. That is unique. There's only one way for that to come out. So the answer is 1/8.


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