Find the mean or expected value of this probability distribution.

Find the standard deviation of this probability distribution.

Use the following for the questions 4 and 5

A sample of 4 people is selected from a group of **six ** people named Ali, Bina, Chris, David, Erin and Frank.

- How many such samples are possible?
- What is the probability a sample containing Bina and Chris is selected.

- How many different simple random samples of size 8 can be selected from a population consisting of 70 people? (you may use the combinations)
- A strabismus surgery has a probability of 0.9 of success in the first attempt and a probability of 0.98 of success in the second attempt. Use the techniques of tree diagrams to find the probability the probability that the surgery will be successful within two attempts. (round four digits after the decimal)

Successful in first attempt = 0.9

Unsuccessful in first attempt= 0.1

Successful in second attempt = 0.98

Unsuccessful in second attempt = 0.02

= 0.9 + 0.1 * 0.98 = 0.998

- A computer manufacturer uses graphic cards made by two companies N and I. They are using the cards made by N in 80% of the computers and made by I on 20% of the computers. They have found that 2% of the cards made by N have been defective and 5% of the cards made by I have been defective. A computer owner has reported a problem with the graphic card. Use the techniques of tree diagrams to find the probability that the card is made by I. (round four digits after the decimal)

For the questions #9, #10, consider a deck of 52 cards as shown below

9. The deck is well shuffled, card is drawn and a card is drawn, find the probability that the card is a face card, i.e. a Jack or Queen, or a King .

10. A game charges $1.00 to play and pays $4.00 if a card drawn from a well shuffled deck such as above is a face card, other wise the the player loses the money. Find the expected expected value of the gain for this player.

You may fill the following table to answer this question