Math

Anna and bob play a game in which Anna begins by rolling a fair dice, after which bob tosses a fair coin. They take turns until one of them wins. Anna wins when she rolls a 6. Bob wins when the coin lands on heads. What is the probability that Anna will win the game?

Well there are a number of ways for Anna to win like 1st it is 1/6 the second way can be 5/6*1/2*5/6*1/2*1/6 etc. Where do i go from here to find an exact number for the probability?

  1. 👍
  2. 👎
  3. 👁
  1. What happens if Anna rolls the 6 and Bob tosses a head? It it considered a tie, or does one or the other automatically win? This will change the probability of Anna winning the game.

    1. 👍
    2. 👎
  2. So, if Ana rolls a 6, does the game end instantly, or does Bob get to flip a coin one last time? If he does, and gets a head, does the game continue or do they declare it a tie?

    Does the question really ask for the probability that Ana wins the game, or does it ask for the probability that she wins the game within a certain number of rounds?

    On Ana's first roll, she has a 1/6 chance of getting a 6.

    In order to get to a second roll, she needs to roll something other than a 6 on her first roll, and Bob needs to get a tails. The probability of that happening is 5/6 * 1/2 = 5/12. Then she has a 1/6 chance of getting a 6 on her 2nd roll, so the probability that Ana wins on her second roll is 5/12*1/6 = 5/72.

    probability that she wins on her third roll is 5/6*1/2*5/6*1/2*1/6=25/864
    So far, the probability that she wins in three rolls or less is 1/6 + 5/72 + 25/864

    This looks like a geometric series, with r=5/12.

    Sum of an infinite geometric series is a1/(1-r) where a1= the first term = 1/6

    a1/(1-r)=(1/6) / (7/12) = 2/7

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Evan buys a new car that costs $23,740. Anna buys the same new car, only she buys the hybrid model. Anna’s hybrid car costs $31,140. Anna pre-pays for gasoline so that the cost for her gasoline will always be $2.40 per gallon

  2. Statistics

    A gambler offers to let you play the following game: he will roll two (fair) dice. If the sum of the two dice is 7, you will lose $8. If the sum of the two dice is 2, you will lose $7. For any other roll, you will win $4. What is

  3. reading comprehension

    Anna has two aunts, Gertie and Samantha. She has one Uncle, jimbo. Jimbo has a nephew on Anna's side of the family, Timothy, who has two children, John and Aubrey. Which of the following indicates the relationship between

  4. English Check

    My Answer: 1. Venture 2. calamity 3. turmoil 4. Flagrant 5. comprehensive 6. rehabilitate 7. fluctuate 8.ponder 9.persevere 10. Conventional We tried to stop Anna from jumping, but her 1)___ disregard of our warnings led to a 2)__

  1. Math

    A game is played using one dice. If the dice is rolled and shows 1, the player wins $1; if it shows 2, the player wins $2; if it shows a 3, the player wins $3. If the die shows 4,5,or 6 the player wins nothing. a.) If there is a

  2. Mathematics for Liberal Arts

    You are on a TV show. You have been asked to either play a dice game five times or accept a $50 bill. The dice game works like this: If you roll a 1, 2 or 3, you win $46. If you roll a 4 or 5, you lose $22. If you roll a 6, you

  3. Math,set

    In a group of 120 students, 72 play chess, 65 play Scrabble and 53 play dice if 35 play both chess and Scrabble, 30 play both chess and dice 21 play both Scrabble and dice and each play at least one of the game. (1) illustrate the

  4. Algebra 2

    Anna and Hannah have $80 each. Their friend offered to invest their money, promising to return a sum r times as great as what they invested. Anna was suspicious, so she invested $20 only, but Hannah invested her entire $80.

  1. Math

    At this year's State Fair, there was a dice rolling game. If you rolled two dice and got a sum of 2 or 12, you won $20. If you rolled a 7,you won $5. Any other roll was a loss. It cost $3 to play one game with one roll of the

  2. algebra

    Gary Glaze requires 25 hours to put a new roof on a house. His​ apprentice, Anna​ Gandy, can reroof the house by herself in 32 hours. After working alone on a roof for 20 ​hours, Gary leaves for another job. Anna takes over

  3. Math

    You are given 9 to 1 odds against rolling a sum of 8 with the roll of two fair dice, meaning you win $9 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game.

  4. MATH

    ANNA HAS 300 AND OJO HAS 1860 IF ANNA SAVES 50 A DAY AND OJO SPENDS 70 A DAY AFTER HOW MANY DAYS WILL THEY HAVE EQUAL AMOUNTS?

You can view more similar questions or ask a new question.