1) Find the conditional probability of the indicated event when two fair dice (one red and...

1) Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. The red one is 4, given that the sum is 9.

2)The Sad State Lottery requires you to select a sequence of four different numbers from 0 through 51. (Order is important.) You are a Winner if your sequence agrees with that in the drawing, and you are a Booby Prize Winner if your selection of numbers is correct, but in the wrong order. What is the probability of being a Booby Prize Winner?

Expert Solution

milcah answered 1 year ago

a) Find the conditional probability of the indicated event when two fair dice (one red and...

a) Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. The sum is 7, given that the green one is either 6 or 2. b) Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. The red one is 3, given that the sum is 5.

Two fair, distinct dice (one red and one green) are rolled. Let A be the event...

Two fair, distinct dice (one red and one green) are rolled. Let A be the event the red die comes up even and B be the event the sum on the two dice is even. Are A,B independent events? Please show work where applicable.

Find the conditional probability, in a single roll of two fair 6-sided dice, that neither die...

Find the conditional probability, in a single roll of two fair 6-sided dice, that neither die is a three,given that the sum is greater than 7.

1. Suppose that two fair dice are rolled. Find the probability that the number on the...

1. Suppose that two fair dice are rolled. Find the probability that the number on the first die is a 6 or the number on the second die is a 2.

6 fair 12-sided dice are rolled. (a) [3 marks] Find the conditional probability that at least...

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.

Two dice are tossed one after the other. What is the conditional probability that the first...

Two dice are tossed one after the other. What is the conditional probability that the first die is six, given that the sum of the dice is seven?

You roll two fair dice. Let A be the event that the sum of the dice...

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...

Two fair dice, one blue and one red, are tossed, and the up face on each...

Two fair dice, one blue and one red, are tossed, and the up face on each die is recorded. Define the following events: E:E: {{ The sum of the numbers is even }} F:F: {{ The difference of the numbers is 3 or more }} Find the following probabilities: P(E)= P(F)= P(EandF)= P(E|F)= P(F|E)=

5. Two fair, distinct dice (one red and one green) are rolled. Let A be the...

5. Two fair, distinct dice (one red and one green) are rolled. Let A be the event the red die comes up even and B be the event the sum on the two dice is 8. Are A,B independent events? According to the American Lung Association 7% of the population has lung disease. Of the people having lung disease 90% are smokers. Of the people not having lung disease 20% are smokers. What are the chances that a smoker has...

probabilities Find the probabilities for each event. Consider rolling a pair of fair dice two times....

probabilities Find the probabilities for each event. Consider rolling a pair of fair dice two times. Let A be the total on the up-faces for the first roll and let B be the total on the up-faces for the second roll. A = {2 on the first roll}, B = {8 or more on the first roll}. A = {2 on the first roll}, B = {8 or more on the second roll}. A = {5 or less on the...

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