Two players A and B play a game of dice . They roll a pair of
dice alternately . The player who rolls 7 first wins . If A starts
then find the probability of B winning the game ?
Consider the following experiment: we roll a fair die twice. The
two rolls are independent events. Let’s call M the number of dots
in the first roll and N the number of dots in the second roll.
(a) What is the probability that both M and N are even?
(b) What is the probability that M + N is even?
(c) What is the probability that M + N = 5?
(d) We know that M + N = 5....
You roll two fair dice. Let A be the event that the sum of the
dice is an even number. Let B be the event that the two results are
different.
(a) Given B has occurred, what is the probability A has also
occurred?
(b) Given A has occurred, what is the probability B has also
occurred?
(c) What is the probability of getting a sum of 9?
(d) Given that the sum of the pair of dice is 9...
1.
Assume we roll 6 dice. What is the probability that the roll
contains:
a. 6 of the same number
b. 3 of one number, 2 of a second number, and 1 non-matching
number
c. 3 pairs of different numbers
Let’s have a dice and a coin. Randomly throw the dice once and
the coin twice. Determine the space of elementary events and P
(A∪B) and check the independence of events A and B, if event A
consists in the fact that on dice we have odd number, B that on
coin we have heads twice and on dice we have number lower than
3.
Let’s have a dice and a coin. Randomly throw the dice once and
the coin twice. Determine the space of elementary events and P
(A∪B) and check the independence of events A and B, if event A
consists in the fact that on dice we have even number, B that on
coin we have heads twice and on dice we have number lower than
3.
suppose you roll two fair dice.
A) what is the probability that you will roll an even number on
the first die AND a 5 on the second die
B) What is the probability that the sum of the numbers on the
two dice is 9?
show all work.
Fair Dice
We roll a fair dice 10 times and register how many times we
obtained 5.
(a) Find the probability to obtain 5 seven times.
(b) Estimate the number of fives that will come out with the
probability 0.35.
(c) What is the probability of geting 30 fives when rolling a
fair dice 45 times?
(d) How many fives will come out with a probability of 0.25,
when rollong a fair dice 45 times?
Suppose we roll two fair dice. Let D1 be the random variable
that denotes the value of the first dice and D2 the sum of the
numbers of both dice.
a) Calculate the joint mass function of D1 and D2.
b) Calculate the conditional mass function of D1 given D2 =
d2.
c) Calculate the conditional mass function of D2 given D1 =
d1.
d) Are the variables D1 and D2 independent? Argue your answer.