Question

In: Statistics and Probability

How many times of “3” are expected to get in rolling an unloaded dice 50 times?...

How many times of “3” are expected to get in rolling an unloaded dice 50 times?

Select one:

a. 25 times

b. 8 times

c. 16.67 times

d. 8.33 times

Expert Solution

Let be a sequence of independent random variables that are all distributed according to a discrete uniform distribution over the numbers 1 to 6. These represent our dice rolls.

Now let be another sequence of variables defined as That is, the indicators that tell us if the i’th die roll comesout 3 or not.

Now we have that and that This implies that these Y-variables are in fact Bernoulli distributed with success parameter 1/6. So each Y is 1 if it’s corresponding die roll yielded 3 and 0 if it didn’t.

Now we can make yet another variable that counts the number of ‘successes’, that is, how many times we get the number 3 in our 50 die rolls. Thus, let
. Now it holds that this sum is binomially distributed with success parameter 1/6 and number of trials equal to 50.

Hence, we may now calculate the expected number of successes (i.e. threes) according to the formula for the expectation of the binomial distribution. That is, times .

So we see that the number of times we would expect the die to land with 3 up is indeed 8.33 out of 50.

option (d) is correct

orchestra answered 1 year ago

1.Two dice are tossed 432 times. How many times would you expect to get a sum...

1.Two dice are tossed 432 times. How many times would you expect to get a sum of 5? ———- 2.Sam is applying for a single year life insurance policy worth $35,750.00. If the actuarial tables determine that she will survive the next year with probability 0.996, what is her expected value for the life insurance policy if the premium is $433.00 ? ————- 3.A raffle is being held at a benefit concert. The prizes are awarded as follows: 1 grand...

Create a simulation layout for rolling 3 dice 627 times. Calculate the probability of the 3...

Create a simulation layout for rolling 3 dice 627 times. Calculate the probability of the 3 adding to 11. ***Use Excel and show formulas used***

Find the probability that: Rolling a fair die 3 times, at least two dice are less...

Find the probability that: Rolling a fair die 3 times, at least two dice are less than 4. Previous answers have suggested 0.875 (189 feasible cases/ 216 total cases). However, from simple trial and error we can see that there are more than 27 cases where this answers fails. For example is the first dice gets a 4 and the 2nd dice gets 4,5,6 and the last dice gets any number, there is already 18 cases here that are not...

Fair Dice We roll a fair dice 10 times and register how many times we obtained...

Fair Dice We roll a fair dice 10 times and register how many times we obtained 5. (a) Find the probability to obtain 5 seven times. (b) Estimate the number of fives that will come out with the probability 0.35. (c) What is the probability of geting 30 fives when rolling a fair dice 45 times? (d) How many fives will come out with a probability of 0.25, when rollong a fair dice 45 times?

You are rolling a fair dice 100 times. Let N be the number of times out...

You are rolling a fair dice 100 times. Let N be the number of times out of 100, when you roll an odd number. What is the most suitable distribution for N? Type one of the following (Poisson, binomial, normal,geometric) . Determine the probability that the number of times N out of 100, when you roll an odd number is 60 or more P ( N ≥ 60 ) = (use R and round to the third decimal place). Which distribution is...

When rolling 2 dice, how many basic outcomes are there? (To answer this, think about how...

When rolling 2 dice, how many basic outcomes are there? (To answer this, think about how many ways can the first dice come up and how many ways can the second dice come up.) a. Using the Counting Principle, how many basic outcomes are there? b. Are they all equally likely? Explain What we’re interested in is sum of the dice, when 2 dice are rolled. c. What are the possible sums when 2 dice are rolled? d. Are they...

. Dice rolling: In c++Write a program that simulates the rolling of two dice. The sum...

. Dice rolling: In c++Write a program that simulates the rolling of two dice. The sum of the two values should then be calculated. [Note: Each die can show an integer value from 1 to 6, so the sum of the two values will vary from 2 to 12, with 7 being the most frequent sum and 2 and 12 being the least frequent sums.] The following table shows the 36 possible combinations of the two dice. Your program should...

Create a simulation layout for rolling three dice 627 times. Calculate the probability of the three...

Create a simulation layout for rolling three dice 627 times. Calculate the probability of the three adding to 11. Use Excel and show formulas used

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...

Consider rolling a fair dice. You keep rolling the dice until you see all of the...

Consider rolling a fair dice. You keep rolling the dice until you see all of the faces (from number 1 to 6) at least once. What is your expected number of rolls?