Probability

posted by .

Suppose that an unfair coin comes up heads 54.1% of the time. The coin is flipped a total of 13 times.

a) What is the probability that you get exactly 6 heads?
b) What is the probability that you get exactly 6 tails?
c) What is the probability that you get at most 9 tails?

  • Probability -

    We would use the binomial expansion of
    (0.541+0.459)^13, where n=13.

    The probability of r occurrences of head is given by (n,r)(0.541)^r(0.459)^(n-r), where (n,r) stands for "n choose r" or
    (n,r)=n!/(r!(n-r)!).

    (a) For 6 heads, r=6, n=13
    P(6H)=(13,6)0.541^6*0.459^7
    =1716*0.02507*.004292
    =0.1847

    (b) exactly 6 tails is the same as exactly 7 heads, so calculate P(7H) using the above formula.

    (c) at most 9 tails means at least 4 heads.

    P(≤9T)
    =P(≥4H)
    =P'(<4H)
    By Kolmogorov's second axiom, we can write
    =1-P(<4H)
    =1-(P(0H)+P(1H)+P(2H)+P(3H))


    Note: You can view Kolmogorov's second axiom at:
    http://mathworld.wolfram.com/KolmogorovsAxioms.html

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    In a game, a player tosses a coin 4 times. If the player gets 3 or 4 heads, he/she wins. What is the theoretical probability of winning this game?
  2. algebra I

    If you toss a coin, the probability of gettig heads is 1/2. If you toss a coin 2 times. the probability of getting heds each time is 1/2*1/2 or (1/2)^2. -Write an expression to represent the probability of tossing a coin 'n' times …
  3. Intro to Probability, please check my work.

    A fair coin is flipped three times. You win $5 every time the outcome is heads. Let the random variable X represent the total number of dollars you win. (a) List the sample space. (b) Determine the probability function of X. ====================== …
  4. probability

    Suppose an unfair coin comes up heads 52.2% of the time if it is flipped. If the coin is flipped 26 times, what is the probability that: a) it comes up tails exactly 12 times?
  5. Stat.

    A trick coin has been weighted so that heads occurs with a probability of p  2 3, and p(tails)  1 3. If you toss this coin 72 times, a. How many heads would you expect to get on average?
  6. math

    Carolyn tested a coin to see if it was evenly weighted. She flipped the coin 100 times and came up with 42 heads and 58 tails. How does the relative frequency of tails to heads compare to the probability of tails in this experiment?
  7. Math

    10. A coin is loaded so that the probability of heads is 0.55 and the probability of tails is 0.45, Suppose the coin is tossed twice and the results of tosses are independent. a.What is the probability of obtaining exactly two heads?
  8. probability

    Adefective coin minting machineproducescoinswhoseprobability ofheadsisarandomvariable P with PDF 1+sin(2πp), if p ∈ [0,1],fP (p)= 0, otherwise. Inessence,aspecificcoinproducedby thismachinewillhavea fixedprobability P = …
  9. math

    Suppose you have an extremely unfair coin: the probability of a head is 1/5, and the probability of a tail is 4/5. If you toss the coin 40 times, how many heads do you expect to see?
  10. statistics

    An unfair coin has a probability of coming up heads of 0.55 the coin is tossed 4 times. What is the probability that it lands heads at least once?

More Similar Questions