Question

In: Statistics and Probability

True or False and explain: a) If a die is rolled twice, the chance of getting...

True or False and explain:

a) If a die is rolled twice, the chance of getting at least on ace is 1/6 + 1/6 =1/3

b) If a coins is tossed twice, the chance of getting at least one head is 100%

Solutions

Expert Solution

Solution:-

(a) False

(b) False

(a) If a die is rolled twice, the chance of getting at least on ace is 1/6 + 1/6 =1/3

if a die is rolled twice, then chance of getting no ace

  

  

If a die rolled twice, then chance of getting at least one ace

  

Hence, Given statement is false

Answer : False

(b)  If a coins is tossed twice, the chance of getting at least one head is 100%

If a coin is tossed twice, the chance of getting no head is

  

If a coin is tossed twice then the chance of getting at least one head is

  

Hence, given statement is false,

Answer: False

Thanks for supporting...

Please give positive rating...


Related Solutions

Rolling a Die If a die is rolled one time, find these probabilities: a. Getting a...
Rolling a Die If a die is rolled one time, find these probabilities: a. Getting a 7 b. Getting an odd number c. Getting a number less than 7 d. Getting a prime number (2, 3, or 5) 4.Rolling a Die If a die is rolled one time, find these probabilities: a. Getting a number greater than 0. b. Getting a number greater than or equal to 3 c. Getting a number greater than 2 and an even number d....
Suppose a 6-sided die and a 7-sided die are rolled. What is the probability of getting...
Suppose a 6-sided die and a 7-sided die are rolled. What is the probability of getting sum less than or equal to 5 for the first time on the 4th roll? Show your work to receive credit.
A fair die is rolled twice. Let X and Y be the smallest and largest, respectively,...
A fair die is rolled twice. Let X and Y be the smallest and largest, respectively, number that appears in the two rolls. (a) Determine the probability mass function of (X, Y). (Write a formula forP(X=i, Y=j)or give a table of values.) (b) Are X and Y independent? (c) Find E(X+Y). (Give your answer as a decimal number.)
If a fair coin is flipped twice and a standard 6 sided die is rolled once,...
If a fair coin is flipped twice and a standard 6 sided die is rolled once, what is the likelihood of getting two 'heads' on the coin and a '1' on the die? ​Express your answer as a percent rounded to the tenth place
A fair die is rolled twice. Let X be the maximum of the two rolls. Find...
A fair die is rolled twice. Let X be the maximum of the two rolls. Find the distribution of X. Let Y be the minimum of the two rolls. Find the variance of Y.
If one dice is rolled (die 1, die 2), find the probability of getting sum less...
If one dice is rolled (die 1, die 2), find the probability of getting sum less than 11? a. What is the probability experiment? Rolling a dice (die 1, die 2) b. What is the event(s)? sum greater than 11 c. What technique can I use to solve this problem? Select an answer d. How do you know you can use that technique? Select an answer f. Find the probability of rolling a sum that is sum less than 11....
Suppose you role a die twice in succession, getting X1 and X2. Then divide them, getting...
Suppose you role a die twice in succession, getting X1 and X2. Then divide them, getting Y=X1X2. Thus, Y is discrete, ranging from a minimum of 1/6 to a maximum of 6. X1 = c(1,2,3,4,5,6) X2 = c(1,2,3,4,5,6) Y = c() for (i in X1) { for (j in X2) { Y = c(Y, i/j) } } Find the mean of the Y. Simulate 10,000 (or more) iid observations Yi(=Xi1Xi2) . Draw the graph of successive average (cumulative mean) of...
An unbiased die is rolled 5 times, what is the probability of: A: Getting exaclty two...
An unbiased die is rolled 5 times, what is the probability of: A: Getting exaclty two 5's in 5 tosses? B: Getting AT LEAST two 3's in 5 tosses? C: Getting AT MOST one 4 in 5 tosses?
A three-sided fair die with faces numbered 1, 2 and 3 is rolled twice. List the...
A three-sided fair die with faces numbered 1, 2 and 3 is rolled twice. List the sample space. S = b.{ List the following events and their probabilities. Write probabilities in non-reduced fractional form A = rolling doubles = { P(A)= / B = rolling a sum of 4 = { P(B)= / C = rolling a sum of 5 = { P(C)= C. Are the events A and B mutually exclusive? If yes, why? If not, why not? D.Are...
(10 marks) A die is rolled twice. Find the joint probability mass function of X andY...
A die is rolled twice. Find the joint probability mass function of X andY if X denotes the value on the first roll and Y denotes the minimum of the values of the two rolls.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT