# 1. Two draws will be made at random from a box containing 5 marbles,

- Two draws will be made at random from a box containing 5 marbles, red, yellow, green, black and blue. The unconditional probability of getting a red marble on the first draw is 1/ 5 . The unconditional probability of getting a red marble on the second draw is 1/5 .
- The chance that the first draw turns out to be the red marble and the second

draw turns to be the red is 1 5´1 5 =1 25when the draws are made __________

replacement, because then the events are________________.

- The chance that the first draw turns out to be the red marble and the second

draw turns to be the red is 0 when the draws are made __________ replacement,

because then the events are________________.

- The chance that at least one of the two draws turns out to be the red marble must

be calculated as 1 -(3 4 ´3 4) =5 16 when the draws are made

______________, because then the events are not ______________.

- The chance that neither of the two draws turns out to be the red marble is 4 / 5 ´3 / 4=3 / 5 when the draws are made_____________________ Replacement, because then the draws are not___________________.
- The chance that neither of the two draws turns out to be the red marble is

4 / 5 ´4 5 =16 25 when the draws are made_____________________

Replacement, because then the draws are ___________________.

Fill in the blanks using one options from each pair below for each sentence.

(with, without) (independent, mutually exclusive)

- A die is tossed 10 times,
a. What is the chance of not getting a 6 spots?

b. What is the chance of getting one of the 6 spots?

c. What is the chance of getting five of the 6 spots?

d. What is the chance of getting at least one of the 6 spots?

- A machine has been designed to toss a coin automatically and keep track of the number of heads. After 1000 tosses, it has 545 heads. Express the chance error both in absolute terms and as a percentage of the number of tosses.

- A computer is programmed to take the sum of 400 draws made at random with replacement from the magic box:

0 | 2 | 4 | 6 | 8 |

- What is the value range for the sum of 400 draws (the possible lowest value and the largest value of the sum of 400 draws)?
- What is the expected value and standard error of the sum of 400 draws?
- What is the chance that the sum is less than 1500? (using the normal approximation)
- A coin will be tossed 400 times. (20 points)
- Find the expected value and standard error for the number of head.
- Estimate the chance of getting more than 220 heads.

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