A die is tossed once, and the face, n, is noted. Then an integer m is...

A die is tossed once, and the face, n, is noted. Then an integer m is selected at random from the set {1,2,···,n}, which depends on the face n. a). Find the probability that m = 3. b). Given that m = 3, what is the probability that n = 6?

Expert Solution

milcah answered 1 year ago

Two fair dice are tossed, and the up face on each die is recorded. Find the...

Two fair dice are tossed, and the up face on each die is recorded. Find the probability of observing each of the following events: A: { The sum of the numbers is even } B: { A 4 appears on at least one of the dice } C: { The difference of the numbers is 2 or less }

Two fair dice are tossed, and the face on each die is observed. Use a tree...

Two fair dice are tossed, and the face on each die is observed. Use a tree diagram to find the 36 sample points contained in the sample space. Assign probabilities to the sample points in part a. Find the probability of each of the following events: A = {3 showing on each die} B = {sum of two numbers showing is 7} C = {sum of two numbers showing is even} Also, for events A, B, and C, which one...

An ordinary six-sided die is tossed once and one slip of paper is randomly drawn from...

An ordinary six-sided die is tossed once and one slip of paper is randomly drawn from a jar containing 5 slips, each of which is lettered U, W, X, Y, or Z. (a) Write the complete sample space that describes all possible outcomes. (b) Determine the probability that the die will show a 6 and that the drawn slip of paper is a U or W. (c) Let A represent the event that the die shows a number greater than...

prove that if an even integer n is subtracted from an odd integer m. then m...

prove that if an even integer n is subtracted from an odd integer m. then m - n is odd.

A die is rolled and, independently, a coin is tossed. Let X be the value of...

A die is rolled and, independently, a coin is tossed. Let X be the value of the die if the coin is H and minus the value of the die if the coin is T. (a) Calculate and plot the PMF of X. (b) Calculate E [X] and var(X) (c) Calculate and plot the PMF of X 2 − 2X. 2. A drunk walks down a street. Assume he starts at block 0. Every 10 minutes, he moves north a...

A) A coin is tossed and a die is rolled. Draw the tree diagram to list...

A) A coin is tossed and a die is rolled. Draw the tree diagram to list out every possible outcome for this sequence of events. How many total outcomes are possible? B) Elementary students are given an ID card that has a picture of their face followed by a 4 digit code. Assuming repetitions are allowed, how many ID cards are possible? C) Six balls are numbered: 1, 2, 3, 5, 8, and 13. A ball is selected, its number...

A die is thrown twice and the sum of the numbers rising is noted to be 6.

A die is thrown twice and the sum of the numbers rising is noted to be 6. Calculate the is the conditional probability that the number 4 has arrived at least once?

A fair die is tossed 120 times. A success is getting a 2 or a 5...

A fair die is tossed 120 times. A success is getting a 2 or a 5 landing face up. (a) Find the probability of getting exactly 40 successes. (b) Does the normal approximation to the binomial apply? If so, use it to approximate the probability of exactly 40 successes.

a die is tossed 60 times and if more than x sixes are obtained then there...

a die is tossed 60 times and if more than x sixes are obtained then there is evidence at 5% level that the die is biased towards six. a)Find x, b)Hence find the probabilty of type 1 error c) Find p(type 2 error if p=0.2)

A fair coin is tossed, and a fair die is rolled. Let H be the event...

A fair coin is tossed, and a fair die is rolled. Let H be the event that the coin lands on heads, and let S be the event that the die lands on six. Find P(H or S).

Question