Find the probability that in 200 tosses of a fair six sided die, a five will...

Find the probability that in 200 tosses of a fair six sided die, a five will be obtained at least 40 times

Expert Solution

Since the no of trails are very large hence we assume it as Normal distribution to calculate probability as

n = number of trials = 200
p = probability of getting a five in one trail = 1/6=0.1667

Since, n*p = 200(1/6) = 33.333

also, n*(1-p) = 166.667 both are greater than 10 hence Normal distribution assumption is correct.

Now, mean = np = 33.33 also,

Standard deviation, s = sqrt(np(1-p)) = sqrt(200(1/6)(5/6)) = 5.27

Now for correction we will use 39.5 instead of X=40 because the question is at least 40 which means 40 has to be included.

Now, Z

Hence using Z table shown below, area above Z=1.27 is

=0.121.

orchestra answered 1 year ago

Suppose you are rolling a fair four-sided die and a fair six-sided die and you are...

Suppose you are rolling a fair four-sided die and a fair six-sided die and you are counting the number of ones that come up. a) Distinguish between the outcomes and events. b) What is the probability that both die roll ones? c) What is the probability that exactly one die rolls a one? d) What is the probability that neither die rolls a one? e) What is the expected number of ones? f) If you did this 1000 times, approximately...

You roll a fair six-sided die and don't look at it. What is the probability that...

You roll a fair six-sided die and don't look at it. What is the probability that it is a 5 given that your friend looks and tells you that it is greater than 2? Leave your answer as a fraction.

You roll a six- sided die. Find the probability of each of the following scenarios a....

You roll a six- sided die. Find the probability of each of the following scenarios a. Rolling a 6 or a number greater than 3 b. Rolling a number less than 5 or an even number c. Rolling a 2 or an odd number

Let Y be the sum of two fair six-sided die. (a) Find the PMF of Y....

Let Y be the sum of two fair six-sided die. (a) Find the PMF of Y. (b) What is the expected value of Y ? (c ) What is the standard deviation of Y ? (d) Interpret the standard deviation you found in the last part in context of the experiment. (e) Find the CDF of Y. (f) Use the CDF of Y to find the probability that the sum of the dice will be strictly between six and ten....

Rolling a fair six-sided die five times could result in the following sample of n =...

Rolling a fair six-sided die five times could result in the following sample of n = 5 observations: What are the mean, variance, and standard deviation?

Approximate the probability that in 205 tosses of a fair die, we will obtain at least...

Approximate the probability that in 205 tosses of a fair die, we will obtain at least 109 fives.

Suppose a red six-sided die, a blue six-sided die, and a yellow six-sided die are rolled....

Suppose a red six-sided die, a blue six-sided die, and a yellow six-sided die are rolled. Let - X1 be the random variable which is 1 if the numbers rolled on the blue die and the yellow die are the same and 0 otherwise; - X2 be the random variable which is 1 if the numbers rolled on the red die and the yellow die are the same and 0 otherwise; - X3 be the random variable which is 1...

Consider rolling both a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6...

Consider rolling both a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6 together. After rolling both dice, let X denote the number appearing on the foursided die and Y the number appearing on the six-sided die. Define W = X +Y . Assume X and Y are independent. (a) Find the moment generating function for W. (b) Use the moment generating function technique to find the expectation. (c) Use the moment generating function technique to find...

Consider a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6, where X...

Consider a fair four-sided die numbered 1-4 and a fair six-sided die numbered 1-6, where X is the number appearing on the four-sided die and Y is the number appearing on the six-sided die. Define W=X+Y when they are rolled together. Assuming X and Y are independent, (a) find the moment generating function for W, (b) the expectation E(W), (c) and the variance Var(W). Use the moment generating function technique to find the expectation and variance.

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.

Question