Counting and Probability #6 (all probability) Name :______
1) If you flip a coin and roll a die, what is the probability that you get tails and then a factor of 6?
2) If you play rock-paper-scissors with a friend, what is the probability you win three turns in a row?
3) Three friends flip a coin. If two people get the same thing and the other is different, than the different one wins. If they are all the same they flip again. What is the probability that someone wins on the first set flips, and that person flipped heads?
3b) What is the probability that in problem #3 it takes 2 flips to get a winner and the winner had tails?
4) The Monkees are playing three baseball games against the Lions, the Tigers, and the Bears(oh my!). They have a 20% chance of beating the Lions, a 40% chance of beating the Tigers, and a 90% chance of beating the Bears(they stink). Answer the questions below :
a) P(3 wins)= ______b) P(3 losses) = ______
c) P(exactly 2 wins) = ______d) P( at least 1 win) = ______
e) P( beating Bears and exactly one more team) = ______
5) If P(x) = .6 , P(y) = .7, P(y after x) = .65. What is :
a) P( x or y) = ______b) P(x and y) = ______
6) John rolls a die until he gets a 5. If the probability that it takes him 8 rolls is , give the ordered pair (x, y).
7) If you were to pick a 4 digit number where all the digits are odd, what is the probability that all 4 digits would be the same?
8) My grandmother had three kids. What is the probability that she had 2 girls and 1 boy?
9) It's magical. It's incredible, and it just arrived! The new handy personal sized box of Bertie Bott's Every Flavor Beans, the jelly bean preferred by Harry Potter. Discover the wild flavors of EARWAX, DIRT, GRASS, BOOGER, SARDINE, BLACK PEPPER and the 2 latest new flavors ROTTEN EGG and BACON. And, everyone's favorite VOMIT. If your box only had 5 Rotten Egg, 6 vomit, 4 Booger, 3 Earwax, and 2 Sardine flavored beans, what would the probability of :
a) P(egg, vomit, booger) = ______b) P(3 vomits) ______
c) P(bacon, worm, grass) = ______d) P(2 in a row NOT vomit) ______
e) P(bacon and egg) = ______e) P(earwax, earwax, earwax, earwax) = ______
10) Pick any integer, add 7, multiply by 3, square it, subtract18. What is the probability the sum of the digits of your new number is divisible by 9?