Two six-sided dice are rolled and the sum is observed. Define events A and B as...

Two six-sided dice are rolled and the sum is observed. Define events A and B as follows:

Event A: The sum is odd.

Event B: The sum is less than 9.

Find P(A or B)

Please use formula P(A) + P(B) - P(A x B)

So I can understand how to use it. Thank you.

Solutions

Expert Solution

$\\$\\ Two six sided dice are rolled and the sum is observed.\\\\ The events $A$ and $B$ are defined as follows :\\ $A:$ The sum is odd\\ $B :$ The sum is less than 9\\\\ Let we denote $(i,j)\hspace{2em}i=1,2,\cdots,6;\hspace{1em}j=1,2,\cdots,6\\ $as ordered pair where $i$ denotes number number on first die \\ and $j$ denotes number on second die.\\\\ Then a simple event corresponding to rolling two six-sided dice can be denoted by $\{(i,j)\}$\\\\ Lowest possible sum we can get is $1+1=2$\\ Highest possible sum we can get is $6+6=12$\\\\ Let we tabulate possible outcomes in the following table for better understanding:$

$\\$\\ \begin{table}[] \begin{tabular}{|c|c|c|} \hline \textbf{Sum} & \textbf{Event} & \textbf{\# favourable outcomes} \\ \hline 2 & \{(1,1)\} & 1 \\ \hline 3 & \{(1,2),(2,1)\} & 2 \\ \hline 4 & \{(1,3),(2,2),(3,1)\} & 3 \\ \hline 5 & \{(1,4),(2,3),(3,2),(4,1)\} & 4 \\ \hline 6 & \{(1,5),(2,4),(3,3),(4,2),(5,1)\} & 5 \\ \hline 7 & \{(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)\} & 6 \\ \hline 8 & \{(2,6),(3,5),(4,4),(5,3),(6,2)\} & 5 \\ \hline 9 & \{(3,6),(4,5),(5,4),(6,3)\} & 4 \\ \hline 10 & \{(4,6),(5,5),(6,4)\} & 3 \\ \hline 11 & \{(5,6),(6,5)\} & 2 \\ \hline 12 & \{(6,6)\} & 1 \\ \hline \end{tabular} \end{table}$

milcah answered 4 months ago

Next > < Previous

Related Solutions

7. Two fair six sided dice are rolled. (i) What is the probability that the sum...

7. Two fair six sided dice are rolled. (i) What is the probability that the sum of the two results is 6? (ii) What is the probability that the larger value of the two results is 4? (iii) What is the probability that the both results are at most 4? (iv) What is the probability that the number 3 appears at least once?

1. Three six-sided dice are rolled. Let X be the sum of the dice. Determine the...

1. Three six-sided dice are rolled. Let X be the sum of the dice. Determine the range of X and compute P(X = 18) and P(X ≤ 4). 2. An urn contains 5 red balls and 3 green balls. (a) Draw 3 balls with replacement. Let X be the number of red balls drawn. Determine the range of X and compute P(X = 3) and P(X 6= 1). (b) Draw 3 balls without replacement. Let Y be the number of...

Two ordinary fair, six-sided dice ate rolled. What is the probability the sum of the numbers...

Two ordinary fair, six-sided dice ate rolled. What is the probability the sum of the numbers on the two dice is 6, given that the number on at least one of the dice is 3? What is the probability the sum of the numbers on the two dice is 8, given that the number on at least one of the dice is 3? What is the probability that the sum of the numbers on the two dice is 9, given...

Two fair six sided dice are rolled. (i) What is the probability that the smaller value...

Two fair six sided dice are rolled. (i) What is the probability that the smaller value of the two results is 3 given that the sum of the two results is 8? (ii) What is the probability that the sum of the two results is at most 5 given that the number 2 appeared at least once? (iii) What is the probability that the sum of the two results is 7 given that exactly one of the two results is...

Two six-sided dice are rolled. (Enter your probabilities as fractions.) (a) What is the probability that...

Two six-sided dice are rolled. (Enter your probabilities as fractions.) (a) What is the probability that the sum of the numbers is greater than eight? Correct: 5/18 (b) What is the probability that the sum of the numbers is greater than eight, given that the first die is a 4??? (c) What is the probability that the first die shows a 4, given that the sum of the numbers is greater than eight???

Finite Math Four fair six sided dice are rolled. Given that at least two of the...

Finite Math Four fair six sided dice are rolled. Given that at least two of the dice land on an odd number, what is the probability that the sum of the result of all four dice is equal to 14?

Lets use Excel to simulate rolling two 8-sided dice and finding the rolled sum. • Open...

Lets use Excel to simulate rolling two 8-sided dice and finding the rolled sum. • Open a new Excel document. • Click on cell A1, then click on the function icon fx and select Math&Trig, then select RANDBETWEEN. • In the dialog box, enter 1 for bottom and enter 8 for top. • After getting the random number in the first cell, click and hold down the mouse button to drag the lower right corner of this first cell, and...

Two dice are rolled together. If the sum of both dice is 6, what is the...

Two dice are rolled together. If the sum of both dice is 6, what is the probability that one will come in 2? (10 points) The average weight of product A produced in a factory is 21 and the standard deviation is 5. Calculate the probabilities P (X> 20) and P (18 <P <22). Calculate the median and standard deviation of the series below. (20 points) Classes 0-2 30 2-4 70 4-6 50 6-8 30 8-10 20 PLEASE SOLVE CORRECTLY...

A regular six-sided die and a regular eight-sided die are rolled to find the sum. Determine...

A regular six-sided die and a regular eight-sided die are rolled to find the sum. Determine the probability distribution for the sum of the two dice. Create a frequency histogram for the probability distribution and determine the expected sum of the two dice.

a. Two dice are rolled; find the probability that the sum of the two numbers is...

a. Two dice are rolled; find the probability that the sum of the two numbers is 7. b. If one card is drawn from a standard deck, find the probability of getting a spade card or a Queen. c. A couple has 3 children, find the probability that exactly one are girls.

Subjects