Question

In: Statistics and Probability

Suppose you roll, two 6-sided dice (refer back to the sample space in the sample space...

Suppose you roll, two 6-sided dice (refer back to the sample space in the sample space notes). Write any probability as a decimal to three place values and the odds using a colon. Determine the following:

a. the probability that you roll a sum of seven (7) is .

b. The odds for rolling a sum of four (4) is .

c. The odds against the numbers on both dice being the same is .

Solutions

Expert Solution

When two 6-sided dice are rolled: Total number of outcomes = 6 x 6 =36

Probability that you roll a sum of seven (7)

= Number of ocutomes that favor a sum of seven / Total number of outcomes

Outcomes that favor a sum of seven : (1,6),(2,5),(3,4),(4,3),(5,2),(6,1)

Number of Outcomes that favor a sum of seven = 6

Probability that you roll a sum of seven (7)

= Number of ocutomes that favor a sum of seven / Total number of outcomes = 6/36 = 1/6 = 0.167

Probability that you roll a sum of seven (7) is 0.167

b .

The odds of rolling a sum of four (4)

= Number of outcomes that favor a sum of four (4) : Number of outcomes that do not favor a sum of (4)

Outcomes that favor a sum of four (4) : (1,3),(2,2),(3,1)

Number of outcomes that favor a sum of four(4) = 3

Number of outcomes that do not favor a sum of (4)

= Total number of outcomes - Number of outcomes that favor a sum of four(4) = 36-3 =33

The ods of rolling a sum of four is

Number of outcomes that favor a sum of four(4) : Number of outcomes that do not favor a sum of (4) = 3 : 33

The odds of rolling a sum of four (4) is 3 : 33 or 1:11

c. The odds against the numbers on both dice being the same is .

Outcomes that favor numbers on both dice being the same = (1,1),(2,2),(3,3),(4,4),(5,5),(6,6)

Number of outcomes that favor numbers on both dice being the same = 6

Number of outcomes that do not favor numbers on both dice being the same

=Total number of outcomes - Number of outcomes that favor numbers on both dice being the same

=36-6=30

The odds against the numbers on both dice being the same is .

Number of outcomes that do not favor numbers on both dice being the same : Number of outcomes that favor numbers on both dice being the same

: 30:6 ; 5:1

The odds against the numbers on both dice being the same is . 30:6 or 5:1

orchestra answered 10 months ago

Next > < Previous

Related Solutions

Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown...

Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown on the dice and Y be the number of dice that show an odd number. a) Find the joint pmf of <X,Y> b) Find the marginals pmf's for both variables. c) Are X and Y independent?

Suppose you roll two 6 sided dice, letting X be the sum of the numbers shown...

Suppose you roll two 6-sided dice, letting X be the sum of the numbers shown on...

Suppose you roll two 6-sided dice, letting X be the sum of the numbers shown on the dice and Y be the number of dice that show an odd number. a) Find the joint pmf of <X,Y> b) Find the maringals pmf's for both variables. c) Are X and Y independent?

You roll two 6-sided dice numbered 1 through 6. Let A be the event that the...

You roll two 6-sided dice numbered 1 through 6. Let A be the event that the first die shows the number 3, let B be the event that the second die shows a 5, and let E be the event that the sum of the two numbers showing is even. Compute P(A)and P(B)and then compute P(AlB). What does this tell you about events A and B?Hint: Remember that the sample space has 36 outcomes! Compute P(ElA)and compute P(E). What does...

Suppose we would roll two standard 6-sided dice. (a) Compute the expected value of the sum...

Suppose we would roll two standard 6-sided dice. (a) Compute the expected value of the sum of the rolls. (b) Compute the variance of the sum of the rolls. (c) If X represents the maximum value that appears in the two rolls, what is the expected value of X? What’s the probability of sum = 7?

You roll two, fair (i.e., not weighted) 6-sided dice once. What is the probability that: 3a....

You roll two, fair (i.e., not weighted) 6-sided dice once. What is the probability that: 3a. The sum is 11 or more? (1 Point) 3b. The sum is 7? (1 Point) 3c. The sum is 6? (1 Point) 3d. Thesumis6or8? (1Point) 3e. The sum is less than 4? (1 Point) 3f. The sum is something other than 2, 7, or 11? (2 Points)

DESCRIPTION Complete the given program to simulate the roll of two 6-sided dice and count the...

DESCRIPTION Complete the given program to simulate the roll of two 6-sided dice and count the number of rolls of each possible roll value (2 to 12). The number of rolls will be input by the user. Count the rolls of each type and then "draw" a histogram by printing a "*" for each roll of each type. The shape of the histogram will follow the "probability distribution" for large numbers of rolls, i.e., it will show more rolls for...

1. (a) List the sample space in the experiment "roll two dice - a red die...

1. (a) List the sample space in the experiment "roll two dice - a red die and a white die." (Hint: Use a table) (b) Find the probability that the sum of the numbers on the two dice is less than seven. (c) Find the probability that the sum of the numbers on the two dice is odd.

Suppose you roll two twenty-five-sided dice. Let X1, X2 the outcomes of the rolls of these...

Suppose you roll two twenty-five-sided dice. Let X1, X2 the outcomes of the rolls of these two fair dice which can be viewed as a random sample of size 2 from a uniform distribution on integers. (b) List all possible samples and calculate the value of the sample mean ¯(X) and variance (s 2 ) for each sample? (c) Obtain the sampling distribution of X¯ from this list by creating a frequency distribution table. You can create a frequency distribution...

. Three Dice of a Kind Consider the following game: You roll six 6-sided dice d1,…,d6...

. Three Dice of a Kind Consider the following game: You roll six 6-sided dice d1,…,d6 and you win if some number appears 3 or more times. For example, if you roll: (3,3,5,4,6,6) then you lose. If you roll (4,1,3,6,4,4) then you win. What is the probability that you win this game?

Subjects