Statistics: Binomial Probability - Coin Toss Problem

Question :
If a fair coin is tossed 200 times, what is the probability that the coin lands tails less than 75 times?

Solution Summary

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A coin is tossed 4 times. Let "A" be the event that the first toss is heads. Let "B" be the event that the third toss is heads.
1. What is the probability that the third toss is heads, given that the first toss is heads?
2. Are "A" and "B" independent? Why or why not?

A coin was flipped twenty times and landed heads fifteen times. Based upon this information, answer the following the question:
If the coin is balanced (fair) what is the probability of a head on the toss?
If the coin is not balanced (not fair), what is the probability of a head on the next toss?
If a fair coin is flipped t

Let N be the number of tosses with a fair coin until tails occurs. What is the characteristic function of N? What is the mean and variance of N? What is the pmf of N? What is the probability that N is an even number?

Use the empirical method to estimate the probability. You count 42 heads when you toss a coin 100 times. If you don't know whether the coin is fair what is the probability the next toss will be a tail?

A cointossed 10,000 times. Heads appears 5100 times. Do you think the
coin is fair at the 0.05% level of significance? at the 0.01% level of
significance?

Consider a state lottery that has a weekly television show. On this show, a contestant receives the opportunity to win $1 million. The contestant picks from 4 hidden windows. Behind each is one of the following: $150,000, $200,000 $1 million, or a "stopper". Before beginning, the contestant is offered $100,000 to stop. Mathemati

Six students will decide which of them are on a committee by flipping a coin. Each student flips the coin and is on the committee if he or she gets a head. What is the probability that someone is on the committee, but not all 6 students?

A) A coin is tossed 20 times. Find probability of getting at least 14 heads.
B) A die is tossed 20 times. Find probability of getting a "1" two times.
C) Three dice are tossed. Find probability that a four shows on exactly two of the dice.

A number N is chosen according to a Poisson distribution with mean 10. A fair coin is then tossed until N +1 heads are obtained. What is the expected number of tosses it will take to stop the experiment?