A fair 6-sided die is rolled and you note whether the number facing up is even...
A fair 6-sided die is rolled and you note whether the number facing up is even or odd. If an even number is rolled then a fair coin is flipped three more times and the number of heads is noted. But if an odd number is rolled then the coin is flipped only twice more and the number of tails is noted.
How many possible outcomes are there for this experiment?
(a) 43 (b) 20 (c) 7 (d) 45 (e) 18 (f) 36 (g) 71 (h) None of the above.
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A fair 6-sided die is rolled and you note whether the number
facing up is even...
A fair (6-sided) die is rolled once, generating a number N. If the number N is...
A fair (6-sided) die is rolled once, generating a number N. If the number N is even, then a fair coin is tossed N + 1 times. If the number N is odd, then a fair coin is tossed 2N times. Let X be the number of heads obtained. Compute E(X). Give a numerical answer as a reduced fraction or a decimal expression accurate to at least 4 decimal places.
7. (3 points) Given a fair 6-sided die. Each time the die is rolled, the probabilities...
7. (3 points) Given a fair 6-sided die. Each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 6 are all equal. 1) If it is rolled once and let A be the event of rolling a number larger than 3 and B be the event of rolling an odd number. What is P(AV B)? 2) If it is rolled three times, what is the probability that the same number shows up in...
Construct a tree diagram of a probability experiment where a 6-sided die is rolled, and then...
Construct a tree diagram of a probability experiment where a 6-sided die is rolled, and then a coin is flipped. a. The probability that there was a number greater than 3 and a tail on the coin. b. The probability that there was an even number on the dies and a tail on the coin. Show all the calculation steps
Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let A...
Suppose that Adam rolls a fair six-sided die and a fair four-sided die simultaneously. Let A be the event that the six-sided die is an even number and B be the event that the four-sided die is an odd number. Using the sample space of possible outcomes below, answer each of the following questions.What is P(A), the probability that the six-sided die is an even number?What is P(B), the probability that the four-sided die is an odd number?What is P(A...
1) Suppose we have a fair 6 sided die and a coin. a) If we roll...
1) Suppose we have a fair 6 sided die and a coin. a) If we roll the die 4 times, the total number of possible outcomes is? b) If we roll the die 2 times then flip the coin 3 times, the total number of possible outcomes is? Show your calculations.
A fair die is rolled 10 times. What is the average number of even number outcomes?
A fair die is rolled 10 times. What is the average number of even number outcomes?
1. Consider a fair four-sided die, with sides 1, 2, 3, and 4, that is rolled...
1. Consider a fair four-sided die, with sides 1, 2, 3, and 4, that is rolled twice. For example, "1,4" would indicate 1 was rolled first and then 4 was rolled second a) Write down the possible outcomes, i.e., the sample space. (b) List the outcomes in the following events: Event A: The number 4 came up zero times. Event B: The number 4 came up exactly one time. . Event C: The sum of the two rolls is odd...
Consider the setting where you first roll a fair 6-sided die, and then you flip a...
Consider the setting where you first roll a fair 6-sided die, and then you flip a fair coin the number of times shown by the die. Let D refer to the outcome of the die roll (i.e., number of coin flips) and let H refer to the number of heads observed after D coin flips. (a) Suppose the outcome of rolling the fair 6-sided die is d. Determine E[H|d] and Var(H|d). (b) Determine E[H] and Var(H).
explainhow to solve Example 33: A die is rolled, find the probability that an even number...
explainhow to solve
Example 33: A die is rolled, find the probability that an even number is obtained. Example 34: Two coins are tossed, find the probability that two heads are obtained. Note: Each coin has two possible outcomes H (heads) and T (Tils) Example 35: Two dice are rolled, find the probability that the sum is a) equal to 1 b) equal to 4 c) less than 13
A six-sided die is to be rolled three times. Assume the rolls are independent and that...
A six-sided die is to be rolled three times. Assume the rolls are independent and that the die is fair. - The probability that all three rolls result in an even number is: A) 1.0 B) 0.75 C) 0.25 D) 0.125 - The probability that at least one of the rolls is an even number is: A) 0.125 B) 0.333 C) 0.750 D) 0.875 - The events A = exactly two of the rolls are even and B = exactly...
7. (3 points) Given a fair 6-sided die. Each time the die is rolled, the probabilities of rolling any of the numbers from 1 to 6 are all equal. 1) If it is rolled once and let A be the event of rolling a number larger than 3 and B be the event of rolling an odd number. What is P(AV B)? 2) If it is rolled three times, what is the probability that the same number shows up in...
1. Consider a fair four-sided die, with sides 1, 2, 3, and 4, that is rolled twice. For example, "1,4" would indicate 1 was rolled first and then 4 was rolled second a) Write down the possible outcomes, i.e., the sample space. (b) List the outcomes in the following events: Event A: The number 4 came up zero times. Event B: The number 4 came up exactly one time. . Event C: The sum of the two rolls is odd...
explainhow to solve
Example 33: A die is rolled, find the probability that an even number is obtained. Example 34: Two coins are tossed, find the probability that two heads are obtained. Note: Each coin has two possible outcomes H (heads) and T (Tils) Example 35: Two dice are rolled, find the probability that the sum is a) equal to 1 b) equal to 4 c) less than 13
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