A gambler has observed from experience that the probability of at least one six when rolling...
A gambler has observed from experience that the probability of at least one six when rolling a fair die four times is slightly larger than the probability of at least one double six when rolling two fair dice 24 times. Do you agree?
A clear explanation will be greatly appreciated.
Homework Answers
Yes the statement is true. The following images contain the complete mathematical reasoning..so check them out!!
cheers :)
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A gambler has observed from experience that the probability of
at least one six when rolling...
3. Determine the following probabilities: (a) Probability you get at least one 3 in four throws...
3. Determine the following probabilities: (a) Probability you get at least one 3 in four throws of a single die. Assume the dice is fair. (b) Probability that you get at least one "double 3" in 24 rolls of a pair of dice. A double 3 is when both dice are 3. (c) You toss two dice. Find the probability that at least one dice is a 4. (d) Find the probability of drawing 2 hearts in succession from a...
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Two fair six-sided dice are rolled. What is the probability that one die shows exactly three more than the other die (for example, rolling a 1 and 4, or rolling a 6 and a 3)
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Suppose you are rolling a fair four-sided die and a fair six-sided die and you are...
Suppose you are rolling a fair four-sided die and a fair six-sided die and you are counting the number of ones that come up. What is the probability that both die roll ones? What is the probability that exactly one die rolls a one? What is the probability that neither die rolls a one? What is the expected number of ones? If you did this 1000 times, approximately how many times would you expect that exactly one die would roll...
4.7 A question about dice. Here is a question that a French gambler asked the mathematicians...
4.7 A question about dice. Here is a question that a French gambler asked the mathematicians Fermat and Pascal at the very beginning of probability theory: what is the probability of getting at least one 6 in rolling four dice? The Law of Large Numbers applet allows you to roll several dice and watch the outcomes. (Ignore the title of the applet for now.) Because simulation-just like real random phenomena-often takes very many trials to estimate a probability accurately, let's...
1. A fair coin is flipped four times. Find the probability that exactly two of the...
1. A fair coin is flipped four times. Find the probability that exactly two of the flips will turn up as heads. 2. A fair coin is flipped four times. Find the probability that at least two of the flips will turn up as heads. 3. A six-sided dice is rolled twice. Find the probability that the larger of the two rolls was equal to 3. 4. A six-sided dice is rolled twice. Find the probability that the larger of...
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Use the "at least once rule to find the probability of getting at least one 4 in six rolls of a single fair die.
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3. Determine the following probabilities: (a) Probability you get at least one 3 in four throws of a single die. Assume the dice is fair. (b) Probability that you get at least one "double 3" in 24 rolls of a pair of dice. A double 3 is when both dice are 3. (c) You toss two dice. Find the probability that at least one dice is a 4. (d) Find the probability of drawing 2 hearts in succession from a...
4.7 A question about dice. Here is a question that a French gambler asked the mathematicians Fermat and Pascal at the very beginning of probability theory: what is the probability of getting at least one 6 in rolling four dice? The Law of Large Numbers applet allows you to roll several dice and watch the outcomes. (Ignore the title of the applet for now.) Because simulation-just like real random phenomena-often takes very many trials to estimate a probability accurately, let's...
23. Calculate the probability of getting exactly two sixes and one five when rolling five dice. Do this in two different ways, as follows. (a) First calculate the probability that two of the five dice land sixes, and then multiply this by the probability that one of the remaining three lands a five. (note: The remaining three dice have only five ways in which they can land.) (b) Next calculate the probability that one of the five dice lands a...
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