Stats 1045 HW 14

There are two options: (i) A die will be rolled 60 times. Each time it shows an ace or a six, you win $1; on the other rolls, you win nothing. (ii) Sixty draws will be made at random with replacement from the box | 1 1 1 0 0 0 | |________________________| On each draw, you will be paid the amount shown on the ticket, in dollars. Which option is better? Or are they the same?

Option (ii) is better.

A pair of dice are thrown. Find the chance that both dice show the same number of spots. Give your answer as a percent with 2 decimals.

16.67

One ticket will be drawn at random from each of the two boxes shown below: (A) | 1 2 3 | |____________| (B) | 1 2 3 4 | |_______________| Find the chance that the number drawn from A is larger than the one from B. Give your answer as a percent rounded to 2 decimal places.

25.00

One event has chance 1/2, another has chance 1/3. Which of the following 2 sentences below are true? -If you want to find the chance that both events will happen, check to see if they are independent. If so, you can multiply the chances. -If you want to find the chance that at least one of the two events will happen, check to see if they are independent. If so, you can multiply the chances. -If you want to find the chance that at least one of the two events will happen, check to see if they are mutually exclusive. If so, you can add the chances. -If you want to find the chance that at least one of the two events will happen, check to see if they are independent. If so, you can add the chances. -If you want to find the chance that both events will happen, check to see if they are independent. If so, you can add the chances. -If you want to find the chance that at least one of the two events will happen, check to see if they are mutually exclusive. If so, you can multiply the chances. -If you want to find the chance that both events will happen, check to see if they are mutually exclusive. If so, you can add the chances.

-If you want to find the chance that both events will happen, check to see if they are independent. If so, you can multiply the chances. -If you want to find the chance that at least one of the two events will happen, check to see if they are mutually exclusive. If so, you can add the chances.

Four draws are going to be made at random without replacement from the box | 1 2 2 3 3 3 | |________________________| Find the chance that | 2 | |_______| is drawn at least once. Give your answer as a percent with 2 decimals.

100.00

One ticket will be drawn at random from each of the two boxes shown below: (A) | 1 2 3 | |____________| (B) | 1 2 3 4 | |_______________| Find the chance that the number drawn from A is smaller than the one from B. Give your answer as a percent rounded to 2 decimal places.

50.00

Three cards are dealt from a well-shuffled deck. Find the chance that the cards are not all diamonds. Give your answer as a percent rounded to 2 decimals.

98.71

The chance of A is 1/3; the chance of B is 1/10. True or false: If A and B are independent, they must also be mutually exclusive.

False

The chance of A is 1/3; the chance of B is 1/10. True or false: If A and B are mutually exclusive, they cannot be independent.

True