for the experiment of rolling an ordinary pair of
dice, find the probability that the sum will be even or a multiple
of 6. ( you may want to use a table showing the sum for each of the
36 equally likely outcomes.)
a) A pair of fair dice is thrown. What is the probability of
rolling a value between 8 and 11, inclusive? (Write your answer as
a decimal rounded to 3 decimal places.)
b) What is the probability of drawing a black face card when a
single card is randomly drawn from a standard deck of 52 cards?
(Write your answer as a decimal rounded to 3 decimal places.)
1.) In rolling a pair of dice, what is the probability of a
total of 4 or less?
2.) A blue die and a red die are tossed together. Find the
probability that the sum is less than 7, given that the blue die
shows a 3.
3.) A fair coin is tossed three times. Find the probability of
getting at least two tails, given that the first toss is tails.
Consider the game consisting of rolling a pair of fair 6-sided
dice and recording the sum. It will cost you $1 to play the game.
If the sumis less than 5, then you will win $3. However, you do not
get your $1 back so your profit is $2. If you roll a sum of
exactly8, thenyou will win $4. However, you do not get your $1 back
so your profit is $3. Otherwise, you lose your $1.
A.What is...
Rolling doubles When rolling two fair, 6-sided
dice, the probability of rolling doubles is 1/6. Suppose Elias
rolls the dice 4 times. Let W = the number of times he
rolls doubles. The probability distribution of W is shown
here. Find the probability that Elias rolls doubles more than
twice.
Value
0
1
2
3
4
Probability
0.482
0.386
0.116
0.015
0.001
6 fair 12-sided dice are rolled.
(a)
[3 marks] Find the conditional probability that at least one
die lands on 3 given that all 6 dice land on different
numbers.
(b)
[2 marks] True or False: If X is the maximum of the 6
numbers from one roll, and Y is the minimum of the 6
numbers from one roll, then X and Y are
independent random variables.
Consider rolling two 6-sided dice.
What is the probability that
at least two of the rolls have a sum that exceeds 6?
at least 7 of the rolls have a sum that is even?
exactly three rolls have a sum that equals 5?
Find the probability that the sum is as stated when a pair of
dice is rolled. (Enter your answers as fractions.) (a) odd and less
than 5 (b) odd or less than 5