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How do you find the probability of a biased coin?
3 Answers
- P(A|B)=P(B|A)P(A)P(B)
- You want to know the probability of P(biased coin|three heads).
- With a fair coin, the probability of three heads is 0.53=1/8.
- The probability of picking the biased coin: P(biased coin)=1/100.
- The probability of all three tosses is heads: P(three heads)=1×1+99×18100.
What is the probability of flipping an unfair coin?
The probability is 0.6 that an “unfair” coin will turn up tails on any given toss.
What makes an unfair coin?
In probability theory and statistics, a sequence of independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin. One for which the probability is not 1/2 is called a biased or unfair coin.
Can you predict a coin toss?
A coin is tossed, and your goal is to predict the outcome (which is either “heads” or “tails”). If the coin is “fair”, then intuitively it doesn’t matter how we predict. But if the coin is “biased”, then predicting one way may be better than the other.
What is the probability of having a fair coin?
Consider the ways to get heads on both of the first two tosses: you can have the unfair coin, or you can have a fair coin and toss heads twice in a row. The probability of having the unfair coin is $\\frac13$. The probability of having a fair coin and tossing heads twice in a row is $\\frac23\\cdot\\frac14=\\frac16$.
How to square fair and unfair coin problem 3?
My reasoning for problem 3 is that if person 1 got the unfair coin it would be 1/3 and to get tails, 0^2. You square it because each trial is dependent of each other? And if person 1 got the fair coin, 2/3, and to get tails, 1/2^2 for the two tosses. So now how would you start doing this problem:
What is the probability of two heads on a coin?
P ( all heads on the four coins) = ( 1 2) 4 = 1 16. P ( either one of the tosses is heads on the two coins) = 1 − P ( no heads on both tosses) = 1 − 1 3 ⋅ 1 3 = 8 9. P ( exactly 3 heads on the four tosses) = 1 4.
What is the probability that a coin is flipped 4 times?
I am stuck on this question. A coin with P ( H) = 1 2 is flipped 4 times and then a coin with P ( H) = 2 3 is tossed twice. What is the probability that a total of 5 heads occurs?