When a certain type of thumbtack is tossed, the probability that it lands tip up is 50%. All possible outcomes when two thumbtacks are tossed are listed. U means the tip is up, and D means the tip is down. UU UD DU DD (a) What is the probability of getting two Ups?  (b) What is the probability of getting exactly one Up?  (c) What is the probability of getting at least one Up (one or more Ups)?

Yahtzee is a game played with 5 dice. Players attempt to score points by rolling various combinations. When all dice show the same number, it’s called Yahtzee and scores 50 points for the first one and 100 points for each successive Yahtzee in the game. a. What is the probability that a person throws a Yahtzee on the very first roll? b. What is the probability that a person throws two Yahtzees on two consecutive rolls?

In the game of keno, if eight spots are marked the player wins if five or more of their spots are selected.  What is the probability of 8 winning spots?  probability of 7 winning spots?  probability of 6 winning spots?  probability of 5 winning spots?  probability of less than 5 winning spots?

You play two games against the same opponent. The probability you win thefirst game is 0.4. If you win the first game, the probability you also win the second is 0.2.If you lose the first game, the probability that you win the second is 0.3. A tie is not anoption.a. Are the two games independent? Explain.b. What’s the probability you lose both games?c. What’s the probability you win both games?d. Let random variable X be the number of games you win. Find the probabilitymodel for X.