Question

Let’s assume that there are two dice, and we will roll one of them, but we...

Let’s assume that there are two dice, and we will roll one of them, but we don’t know which one. The probability of rolling either dice is 1/2. One of them is fair in the sense that all 6 outcomes are equally likely. The other die gives probability 1/3 to numbers 1 through 3 and zero probability to numbers 4-6.

a-)The first roll was a 4. What is the probability that it was the fair die?

b-)The first roll was a 3. What is the probability that it was the fair die?

Hint(Bayes Rule)

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
We roll two fair 6-sided dice, A and B. Each one of the 36 possible outcomes...
We roll two fair 6-sided dice, A and B. Each one of the 36 possible outcomes is assumed to be equally likely. a. Find the probability that dice A is larger than dice B. b. Given that the roll resulted in a sum of 5 or less, find the conditional probability that the two dice were equal. c. Given that the two dice land on different numbers, find the conditional probability that the two dice differed by 2.
Consider rolling two fair six-sided dice. a) Given that the roll resulted in sum of 8,...
Consider rolling two fair six-sided dice. a) Given that the roll resulted in sum of 8, find the conditional probability that first die roll is 6. b) Given that the roll resulted in sum of 4 or less, find the conditional probability that doubles are rolled. c) Given that the two dice land on different numbers, find the conditional probability that at least one die is a 6.
Let’s say that you have three dice that are different colors; one is blue, one is...
Let’s say that you have three dice that are different colors; one is blue, one is pink, and one is grey. Figure out the probability of each of the following outcomes, showing as much work as you can: b) rolling a 3 or 4 on the pink die AND a 3 or 4 on the grey die on the same roll
A bag contains 1000 identical looking six-sided dice. All are fair dice except one which produces...
A bag contains 1000 identical looking six-sided dice. All are fair dice except one which produces a ‘6’ with probability 0.4 with all other outcomes being equally likely. I put my hand in the bag and select a die at random. I roll it n times and every roll is a ‘6’. What is the probability (in terms of n) that I chose the unfair die? What is the least value of n such that the probability I actually have...
Rolling Snake Eyes We roll two six-sided dice d1 and d2. What is the probability that...
Rolling Snake Eyes We roll two six-sided dice d1 and d2. What is the probability that we roll two ones. (i.e., the probability that d1=d2=1). We roll two six-sided dice d1 and d2 and at least one of the dice comes up as a one. What is the (conditional) probability that we roll two ones. We roll two six-sided dice d1 and d2 and at least one of the dice comes up as a one. What is the (conditional) probability...
We roll three fair six-sided dice. (a) What is the probability that at least two of...
We roll three fair six-sided dice. (a) What is the probability that at least two of the dice land on a number greater than 4? (b) What is the probability that we roll a sum of at least 15? (c) Now we roll three fair dice n times. How large need n be in order to guarantee a better than 50% chance of rolling a sum of at least 15, at least once?
Consider an experiment where we roll 7 fair 6-sided dice simultaneously (the results of the dice...
Consider an experiment where we roll 7 fair 6-sided dice simultaneously (the results of the dice are independent from each other). (a) What is the probability that exactly 3 of the dice are greater than or equal to 5? (b) Suppose now that each of the 7 6-sided dice are weighted the same such that the probability of rolling a 6 is 0.5, and every other side that is not a 6 has equal probability of being rolled. If we...
Question I: You roll 2 fair dice, one red and one green. a) What is the...
Question I: You roll 2 fair dice, one red and one green. a) What is the probability that the red die does land on 4? does not land on 4? b) What is the probability that either die lands on 4? that neither die lands on 4? c) What is the probability that the sum of the dice is 2? 3? 4? 5? 6? 7? 8? 9? 10? 11? 12?
QUESTION 5: A 4-sided die is used for some games. This die can only land on...
QUESTION 5: A 4-sided die is used for some games. This die can only land on the numbers 1, 2, 3, or 4. All these outcomes are equally likely. Suppose we roll two 4-sided dice. a. (3 pts) Write out the sample space (the set of all the ways in which the two dice could land). b. (2 pts) What is the probability that at least one of the dice shows a 3? c. (3 pts) Suppose we compute the...
Suppose you roll two six-sided dice at once, one yellow and the other green. Find the...
Suppose you roll two six-sided dice at once, one yellow and the other green. Find the probability that: (1) The yellow die shows 3 and the green shows 5. (2) The yellow die is even and the green shows 1. (3) The sum of the two numbers shown is 6.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT