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39
Probability - Gravner-64.d
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (d) Find an expression for $P(Y>10)$.
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(d) Find an expression for $P(Y>10)$.
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40
Probability - Gravner-64.c
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (c) Find an expression $P$($X\geqslant 6$).
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(c) Find an expression $P$($X\geqslant 6$)...
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41
Probability - Gravner-64.b
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (b) Write down the probability mass function of Y.
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(b) Write down the probability mass functi...
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42
Probability - Gravner-64.a
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3. (a) Write down the probability mass function of X.
Roll a fair die repeatedly. Let X be the number of 6's in the first 10 rolls and let Y the number of rolls needed to obtain a 3.(a) Write down the probability mass functi...
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43
Probability - Gravner-63
You roll a die, your opponent tosses a coin. If you roll $6$ you win; if you do not roll $6$ and your opponent tosses Heads you lose; otherwise, this round ends and the game repeats. On the average, how many rounds does the game last?
You roll a die, your opponent tosses a coin. If you roll $6$ you win; if you do not roll $6$ and your opponent tosses Heads you lose; otherwise, this round ends and the ...
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45
Probability - Gravner-61
Suppose that the probability that a person is killed by lighting in a year is, independently, $1/(500)$ million. Assume that the US population is $300$ million.
Suppose that the probability that a person is killed by lighting in a year is, independently, $1/(500)$ million. Assume that the US population is $300$ million.
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47
Probability - Gravner-59
Let $X$ be the number shown on a rolled fair die. Compute EX,E(X2), and Var(X).
Let $X$ be the number shown on a rolled fair die. Compute EX,E(X2), and Var(X).
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48
Probablity-Gravner-58
Let $X$ be a random variable with $P(X=1) =0.2,P(X=2)=0.3$, and $P(X=3)=0.5$. What is the expected value of $X$?
Let $X$ be a random variable with $P(X=1) =0.2,P(X=2)=0.3$, and $P(X=3)=0.5$. What is the expected value of $X$?
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49
Probability - Gravner-56
Let $X$ be a random variable with $P(X=1) =0.2, P(X=2) = 0.3$, and $P(X=3) = 0.5$. What is the expected value of $X$?
Let $X$ be a random variable with $P(X=1) =0.2, P(X=2) = 0.3$, and $P(X=3) = 0.5$. What is the expected value of $X$?
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51
Probability - Gravner-55
An urn contains $20$ balls numbers $1,.........20$. Select $5$ balls at random, without replacement. Let X be the largest number among selected balls. Determine its p.m.f. and the probability that at least one the selected numbers is $15$ or more.
An urn contains $20$ balls numbers $1,.........20$. Select $5$ balls at random, without replacement. Let X be the largest number among selected balls. Determine its p.m.f...
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52
Probability - Gravner-54
Let $X$ be the number of Heads in $2$ fair coin tosses. Determine its p.m.f.
Let $X$ be the number of Heads in $2$ fair coin tosses. Determine its p.m.f.
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55
Probability - Gravner-52.b
Five married couples are seated at random around a round table. (b) Compute the probability that at most one wife does not sit next to her husband.
Five married couples are seated at random around a round table.(b) Compute the probability that at most one wife does not sit next to her husband.
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56
Probability - Gravner-52.a
Five married couples are seated at random around a round table. (a) Compute the probability that all couples sit together(i.e., every husband-wife pair occupies adjacent seats).
Five married couples are seated at random around a round table.(a) Compute the probability that all couples sit together(i.e., every husband-wife pair occupies adjacent s...
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57
Probability - Gravner-51.b
Ten fair dice are rolled. What is the probability that: (b) Each of the number $1,2,3$ appears exactly twice, while the number $4$ appears four times.
Ten fair dice are rolled. What is the probability that:(b) Each of the number $1,2,3$ appears exactly twice, while the number $4$ appears four times.
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58
Probability - Gravner-51.a
Ten fair dice are rolled. What is the probability that: a) At least one $1$ appears.
Ten fair dice are rolled. What is the probability that:a) At least one $1$ appears.
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59
Probability - Gravner-51.c
Ten fair dice are rolled. What is the probability that: (c) Each of the number $1,2,3$ appears at least once.
Ten fair dice are rolled. What is the probability that:(c) Each of the number $1,2,3$ appears at least once.
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