4. Suppose we roll
N
dice, where
N
is a random number, with
P (
N
=
i
) = 2
−
i
for
i
≥
1
. The
sum of the dice is denoted by
S
. Find the probability that:
(a) (5 points)
N
= 2
given
S
= 4
;
(b) (5 points)
N
is even;
(c) (5 points)
S
= 4
given
N
is even.
4. Suppose we roll N dice, where N is a random number, with P ( N...
A random number N of dice is thrown. Let Ai be the event that N = 1, and assume that P(A) 2-1i 2 1. The sum of the scores is S. Find the probability that: (a) N- 2 given S-4; (b) N 2 given that S 4 and the first die showed 1
3) We roll 2 fair dice. a) Find the probabilities of getting each possible sum (i.e. find Pr(2), Pr(3), . Pr(12) ) b) Find the probability of getting a sum of 3 or 4 (i.e.find Pr(3 or 4)) c) Find the probability we roll doubles (both dice show the same value). d) Find the probability that we roll a sum of 8 or doubles (both dice show the same value). e) Is it more likely that we get a sum...
#5. Suppose we roll three tetrahedral dice that have 1, 2, 3, and 4 on their four sides. Find the probability distribution for the sum of the three sides.
We throw a random number N of dice where N has the distribution given by the probability mass function fv(n) -2-" for n-1,2,3,-... For each i 1,2, 3, 4,5,6, evaluate the probability that the largest number shown by any die is i.
We roll 2 dice and sum the numbers on the faces. a) What is the probability that we roll a 5? b) What is the probability that we roll a 2 or a 3? c) What is the probability that we roll at least a 10? d) What is the probability that we roll at most a 5? e) What is the probability that we roll an even sum? f) What is the probability that we roll either an even...
Roll 10 dice. Find probability sum of dice is 42. (dice are 6-sided. Min roll = 10. Max roll = 120.) (number of possible rolls = 6^10 = 60466176) = s^n number of favorable rolls = number of ways dice add to 42 [(number of favorable rolls)/(number of possible rolls)] = [Probability sum is 42] You must find number of favorable rolls. Given number of dice(n), sides(s), and sum of roll (r) as n = 10, s = 6, and...
8. We roll two fair dice. (1) Given that the roll results in a sum of 6 or less, what is the conditional probability that doubles are rolled? A "double" means that two dice have the same number (2) Given that the two dice land on different numbers, what is the conditional proba- bility that at least one die roll is a 1?
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y. Let random variable Z be (X+Y). The range of Z will be from 2-8. 1.(2.5 points) Find E(Z). 2. (2.5 points) Find P(Z = 71Z > 5). 3.(2.5 points) What is the probability that you have to play the game 4 times before you roll Z=7? 4. (2.5...
Suppose you roll two 4 sided dice. Let the probabilities of the first die be represented by random variable X and those of the second die be represented by random variable Y. Let random variable Z be (X+Y). The range of Z will be from 2-8. 1.(2.5 points) Find E(Z). 2. (2.5 points) Find P(Z = 71Z > 5). 3.(2.5 points) What is the probability that you have to play the game 4 times before you roll Z=7? 4. (2.5...
1. Roll an even dice and observe the number N on the uppermost face. Then toss a fair coin N times and observe X, the total number of heads that appear in N tosses. (i) Write down the conditional probability mass function pX|N(·|3). (ii) What is P(X = 5)? (iii) What is E(X)?