**STAT
16 TEST 2**

- How many words can be formed from the letters F AILURE if �the F remains fixed in first position the vowels are next to one another? What is the probability of randomly forming a word that fits this condition?

- The probability of winning GAME ONE .45 and the probability of winning at GAME TWO is .75, and the probability of winning at both games is .25
- Find the probability of winning at least one of the games.
- Find the probability of losing both.

- Page 184 # 4.130

- The probability that it will rain is .8. Given that it rains the probability that the weather forecaster will predict rain is 0.9. Given that it does not rain the probability the weather forecaster does not predict rain is 0.2. find the probability that:
- It will rain and the weather forecaster will predict rain
- It will not rain and the weather forecaster will not predict rain

- Page 184 # 4.138

- A game consists of randomly
drawing one card from a standard deck of 52 cards. It costs $2 to play. If
a diamond is drawn your return is $3.50, if a black card between 3 and 7
inclusive is drawn your return is $10. Any other card you lost the $2.
Define a probability function then find the expected profit (mean) and
variance for this game. Note that Aces count as one.