Roll two dice 48 times and record the sum of the spots
on the top faces as you roll. Then construct a probability
distribution for your 48 sums. Using the probability distribution,
you constructed, find the mean number of spots. (If you don't have
two dice, then cut out 6 pieces of paper with each being the same
size and with #1,2,3,4,5,6 written on them. Place the pieces of
paper in a hat or bowl. Pull out a number, then...
Two fair dice are tossed. Let A be the maximum of the two
numbers and let B be the absolute difference between the two
numbers. Find the joint probability of A and B. Are A and B
independent? How do you know?
Q2. Two fair dice are tossed and recorded
(a) What is the probability that the sum of the two dice is at most
10?
(b) Given that the sum is an even number, what is the
probability that the sum of two dice is 6 or 10?
Take 3 dice and throw these dice 30 times. Let X be the sum of
the number of dots on upper faces of the dice.
Obtain probability distribution of X. Also find mean and
variance.
2. Three fair dice are rolled. Let X be the sum of the 3
dice.
(a) What is the range of values that X can have?
(b) Find the probabilities of the values occuring in part (a);
that is, P(X = k) for each k in part (a). (Make a table.)
3. Let X denote the difference between the number of heads and
the number of tails obtained when a coin is tossed n times.
(a) What are the possible...
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...