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How do you find the probability distribution of x if a fair coin is tosses four times and x is the PRODUCT of the number of heads times the number of tails?
There are 16 possible outcomes, each of which is equally likely. So each has a probability of 1/16
HHHH: X = H*T = 4*0 = 0
HHHT: X = H*T = 3*1 = 3
HHTH: X = H*T = 3*1 = 3
HTHH: X = H*T = 3*1 = 3
THHH: X = H*T = 3*1 = 3
HHTT: X = H*T = 2*2 = 4
HTHT: X = H*T = 2*2 = 4
HTTH: X = H*T = 2*2 = 4
THHT: X = H*T = 2*2 = 4
THTH: X = H*T = 2*2 = 4
TTHH: X = H*T = 2*2 = 4
HTTT: X = H*T = 1*3 = 3
THTT: X = H*T = 1*3 = 3
TTHT: X = H*T = 1*3 = 3
TTTH: X = H*T = 1*3 = 3
TTTT: X = H*T = 0*4 = 0
So, the probability distribution function of X is
f(X = 0) = 1/16
f(X = 1) = 4/16 = 1/4
f(X = 2) = 6/16 = 3/8
f(X = 3) = 4/16 = 1/4
f(X = 4 = 1/16
and
f(X = x) = 0 for all other x
What else can I help you with?
Is tossing a fair coin one hundred times and counting the number of heads an example of a binomial experiment?
Yes. You are measuring the number of 'successes', x, (in this case the number of heads) out of a number of 'trials', n, (in this case coin tosses) that has an assumed probability, p, (in this case 50% expressed as 0.5) of happening. This phenomenon follows a binomial distribution. Apply the binomial distribution to evaluate whether the the probability of x success from n trials with probability p of occurring is within a pre-determined 'acceptable' limit. Let's say you observe 54 heads in 100 tosses and you wonder if the coin really is fair. From the binomial distribution, the probability of getting *exactly* 54 heads from 100 tosses (assuming that the coin *is* fair & should have 0.5 chance of landing on either side) is 0.0580 or 5.8%. Note that this is not the same probability as 54 heads *in a row*. Most statisticians would agree that 5.8% is too large and conclude that the coin is fair.
What is the probability of getting both tails on two tosses of a coin?
The probability of two tails on two tosses of a coin is 0.52, or 0.25.
How does increasing the number of tosses of a coin affect the average size of the deviation?
It's an important principle or probability. The more coin tosses there are, the more chance there is for an expected outcome.
What is the probability of getting no tails on two tosses of a coin?
The probability is 1/4
If you toss a coin 3 times what is the probability that it will land on heads 3 times?
The probability of getting heads on three tosses of a coin is 0.125. Each head has a probability of 0.5. Since the events are sequentially unrelated, simply raise 0.5 to the power of the number of tosses (3) and get 0.125, or 1 in 8.
What is the probability of obtaining 45 or fewer heads in 100 tosses of coin?
To determine the probability of obtaining 45 or fewer heads in 100 tosses of a fair coin, you can use the binomial distribution model. The number of trials (n) is 100, and the probability of success (getting heads) on each trial (p) is 0.5. The cumulative probability can be calculated using statistical software or a binomial probability table, yielding a result near 0.5, as 45 heads is close to the mean of 50 heads expected in 100 tosses. For precise calculations, employing the normal approximation to the binomial distribution can also provide an estimate.
How many heads are probable in a series of ten tosses?
In a series of ten coin tosses, each toss has two possible outcomes: heads or tails. The expected number of heads can be calculated as the product of the number of tosses and the probability of getting heads in a single toss, which is 0.5. Therefore, in ten tosses, the expected number of heads is 10 × 0.5 = 5 heads. However, the actual number of heads can vary due to the randomness of each toss.
When tossing a fair coin the probability of getting three heads in a row is?
In a large enough number of tosses, it is a certainty (probability = 1). In only the first three tosses, it is (0.5)3 = 0.125
Is tossing a fair coin one hundred times and counting the number of heads an example of a binomial experiment?
Yes. You are measuring the number of 'successes', x, (in this case the number of heads) out of a number of 'trials', n, (in this case coin tosses) that has an assumed probability, p, (in this case 50% expressed as 0.5) of happening. This phenomenon follows a binomial distribution. Apply the binomial distribution to evaluate whether the the probability of x success from n trials with probability p of occurring is within a pre-determined 'acceptable' limit. Let's say you observe 54 heads in 100 tosses and you wonder if the coin really is fair. From the binomial distribution, the probability of getting *exactly* 54 heads from 100 tosses (assuming that the coin *is* fair & should have 0.5 chance of landing on either side) is 0.0580 or 5.8%. Note that this is not the same probability as 54 heads *in a row*. Most statisticians would agree that 5.8% is too large and conclude that the coin is fair.
The experimental probability of a coin landing on heads is 712. if the coin landed on tails 30 timefind the number of tosses?
The experimental probability of a coin landing on heads is 7/ 12. if the coin landed on tails 30 timefind the number of tosses?
Find the probability of heads on three consecutive tosses of a coin?
The number of total outcomes on 3 tosses for a coin is 2 3, or 8. Since only 1 outcome is H, H, H, the probability of heads on three consecutive tosses of a coin is 1/8.
What is the probability of getting a number less than 3 tosses of a single die?
2 out of 6
What is the probability of getting both tails on two tosses of a coin?
The probability of two tails on two tosses of a coin is 0.52, or 0.25.
How does increasing the number of tosses of a coin affect the average size of the deviation?
It's an important principle or probability. The more coin tosses there are, the more chance there is for an expected outcome.
What is the probability of getting three sixes in five tosses of a die?
The probability is 0.0322
What is the probability of getting no tails on two tosses of a coin?
The probability is 1/4
What is the probability of getting 2 heads on all 3 tosses?
The probability is 0, since there will be some 3-tosses in which you get 0, 1 or 3 heads. So not all 3-tosses will give 2 heads.
