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Assigning Probabilities A die is weighted so that a six cannot appear. All the other faces occur with the same probability. What probability should be assigned to e...

Question

Assigning Probabilities A die is weighted so that a six cannot appear. All the other faces occur with the same probability. What probability should be assigned to each face?

Assigning Probabilities A die is weighted so that a six cannot appear. All the other faces occur with the same probability. What probability should be assigned to each face?



Answers

What is the probability of rolling an even number of dots with a fair, six-sided die numbered one through six?

Okay, So what is the probability that a fair diet comes up six minutes roll? So the probability that the dice six to die roll six is the number all favorable. Favorable outcomes, No comes. How about the turtle? Every number. Well possible. Possible outcomes. So in this case, the number off favorable outcomes is only when he comes up. Six. There's only one favor. What outcome? Over the over the possible amount of outcomes. So a guy has six faces that's once for 56 so, therefore, is one over six.

So we want to know the probability that are dying never comes up, even one rolled six times. First, we get all possible outcomes when we roll the dice six times, that is 6 to 6 power. And this is because there are six sides and a die, and it is rolled six times. And this is by the product rule. So this is all possible outcomes when bowling six times six times. Then we get all possible outcomes when we roll the dice six times and every world gives us an odd number. That is 3006 by the product rule as well, since there are three odd sites in A in a dye and it has rolled six times. So it's all possible. Um, outcomes went rolling six times, and every it's every every roll is on. Therefore, the probability is three to the sixth, divided by 6 to 6, and that is equal to one over 64 penned isms, upping the probability that our dai never comes up. Even one rolled six times

If you were ruling a guy pulled that number of fees twice is likely as a even number. Please think about what are welcome. But we have the outcome. 123456 A probability one. Plus, I go to that cross, probably of six. Because one we could put every probability in terms of one probability. Because we know an odd number, face is twice as likely as it even number face. So the probability that too coming up is 1/2 of a probability of one time. So this is gonna turn into the probability of one. What's 1/2 The probability one probabilities. One. Because all the odd number probabilities are the same. We're gonna have 123 times the probability of one plus three halves comes a probability of one equals one. Well, what does this give us? This gives us 4.5 ax equals one X is gonna equal one divided by 4.5. Um, which is going to give us two nights? Now let's see if this makes sense. There's the probability of all odd members. So just call that what p odd equals two NYSE ability, even number is gonna equal one night. Let's make sense, Logan of two knives for Nance 697 98 lines and wall that the

All right. So here told that to fair days of global tasked with probability that the some of the this is seven you call seven before, about all the possible combinations where this could be the case. How you could roll. 16 25 three and a Ford for three, 52 or six and the one that can give us 123456 combinations Ability of any of these events happening, it's the same. It's one of her. Six times, 1/6. So I'm right. Probability equals 1/36. Now, if six times 1/36 is gonna give us one six.


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