Question

In: Statistics and Probability

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.

Solutions

Expert Solution

Answer:-

Given that:-

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

Here, we have to use the normal approximation for finding required probability.

We have to find P(X≥109) = P(X>108.5) (by using continuity correction)

We are given

n = 205

p = P(5) = 1/6 = 0.1667

q = 1 - p = 1 - 0.1667 = 0.8333

Mean = np = 205*0.1667 = 34.1735

SD = sqrt(npq) = sqrt(205*0.1667*0.8333) = 5.336364

P(X>108.5) = 1 - P(X<108.5)

Z = (X - mean)/SD

Z = (108.5 - 34.1735)/ 5.336364

Z = 13.9283

P(Z<13.9283) = P(X<108.5) = 1

(by using z-table or excel)

P(X>108.5) = 1 - P(X<108.5)

P(X>108.5) = 1 - 1

P(X>108.5) = 0.0000

Required probability = 0.0000


Related Solutions

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
A fair red die and a fair green die are rolled. (a) What is the probability...
A fair red die and a fair green die are rolled. (a) What is the probability that the sum of the numbers is even? (b) What is the probability that the number on the red die is more than the number on the green die? (c) What is the probability that the number on the red die is twice the number on the green die? (d) What is the probability that the number on the red die is different from...
Suppose that we roll a die 166 times. What is the approximate probability that the sum...
Suppose that we roll a die 166 times. What is the approximate probability that the sum of the numbers obtained is between 544 and 606, inclusive. (if possible, could you explain the steps/ state theorems used). Thank you :)
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...
We flip a fair coin 20 times. Find the probability that we obtain between 8 and...
We flip a fair coin 20 times. Find the probability that we obtain between 8 and 17 heads, inclusively. Show work and please explain to someone that hardly understands statistics!
Toss a fair coin repeatedly. Let N1 be the number of tosses required to obtain heads...
Toss a fair coin repeatedly. Let N1 be the number of tosses required to obtain heads followed immediately by tails. Let N2 be the number of tosses required to obtain two heads in a row. (A) Should N1 and N2 have the same expected value? If not, which expected value should be larger? Explain your answers. (B) Find the probability mass function of N1. (C) Find the expected value of N1. (D) Find the probability mass function of N2. (E)...
A fair coin is flipped repeatedly. (a) (6pts) Suppose we hope that with probability at least...
A fair coin is flipped repeatedly. (a) (6pts) Suppose we hope that with probability at least 0.9 the frequency of heads showing up is between 0.4 and 0.6. Use Chebyshev’s inequality to estimate at least how many times the coin should be flipped. (b) (6pts) Suppose we hope that with probability at least 0.95 the frequency of heads showing up is between 0.4 and 0.6. Use the central limit theorem to estimate at least how many times the coin should...
Five fair die are rolled. What is the probability of at most two of the dice...
Five fair die are rolled. What is the probability of at most two of the dice coming up a one or a six? Your workings should show the use of appropriate laws and formulae — do not provide a purely arithmetic answer.
Suppose a single fair die is rolled. Find the probability that it is a 2, given...
Suppose a single fair die is rolled. Find the probability that it is a 2, given that it is an odd number. The probability is
What is the probability that you win at least twice if you purchase nine tickets? .205...
What is the probability that you win at least twice if you purchase nine tickets? .205 statistics
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT