Suppose Tori has an unfair coin which lands on Tails with probability 0.28 when flipped. If she flips the coin 10 times, find each of the following:
Question 5 options:
P(No more than 3 Tails)
P(Exactly 1 Tail)
P(At least 5 Tails)
P(Less than or equal to 2 Tails)
P(At least 1 Tail)
The standard deviation of the number of Tails
The mean number of Tails
P(Exactly 4 Tails)
P(No Tails)
P(More than 3 Tails)
1. 0.1798
2. 0.7021
3. 2.8
4. 0.1181
5. 0.1456
6. 0.0374
7. 0.9626
8. 0.2979
9. 0.4378
10. 1.42
Binomial distribution,
n=10
p=0.28
q=1-0.28=0.72
mean=np
variance=npq
std dev=sqrt(npq)
Exactly r successes
=P(r)
=nCr p^r q^(n-r)
Work out each of the above problems and you will find a match.
For example, the first one:
P(no more than 3 tails)
=P(0)+P(1)+P(2)+P(3)
=0.037+0.146+0.255+0.264
=0.7021 (choice #2)
etc.
Post your answers for an answer check.
0.9626
To find the probability of various outcomes when flipping an unfair coin, we can use the binomial distribution formula. The binomial distribution is used to calculate the probability of obtaining a specific number of successes (in this case, the number of Tails) in a fixed number of trials (in this case, 10 flips), given a probability of success for each trial (in this case, 0.28).
Let's go through each question one by one:
1. P(No more than 3 Tails): This refers to the probability of getting 0, 1, 2, or 3 Tails. To find this probability, we can calculate the individual probabilities of getting 0, 1, 2, and 3 Tails and sum them up. Using the binomial distribution formula, we get:
P(No more than 3 Tails) = P(0 Tails) + P(1 Tail) + P(2 Tails) + P(3 Tails)
2. P(Exactly 1 Tail): This refers to the probability of getting exactly 1 Tail. Using the binomial distribution formula, we get P(Exactly 1 Tail).
3. P(At least 5 Tails): This refers to the probability of getting 5, 6, 7, 8, 9, or 10 Tails. To find this probability, we can calculate the individual probabilities of getting 5, 6, 7, 8, 9, and 10 Tails and sum them up.
4. P(Less than or equal to 2 Tails): This refers to the probability of getting 0, 1, or 2 Tails. To find this probability, we can calculate the individual probabilities of getting 0, 1, and 2 Tails and sum them up.
5. P(At least 1 Tail): This refers to the probability of getting 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10 Tails. To find this probability, we can calculate the individual probabilities of getting 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 Tails and sum them up.
6. The standard deviation of the number of Tails: The standard deviation of a binomial distribution is given by the formula sqrt(n * p * (1 - p)), where n is the number of trials and p is the probability of success for each trial. In this case, n = 10 and p = 0.28.
7. The mean number of Tails: The mean of a binomial distribution is given by the formula n * p, where n is the number of trials and p is the probability of success for each trial. In this case, n = 10 and p = 0.28.
8. P(Exactly 4 Tails): This refers to the probability of getting exactly 4 Tails. Using the binomial distribution formula, we get P(Exactly 4 Tails).
9. P(No Tails): This refers to the probability of getting no Tails. Using the binomial distribution formula, we get P(No Tails).
10. P(More than 3 Tails): This refers to the probability of getting 4, 5, 6, 7, 8, 9, or 10 Tails. To find this probability, we can calculate the individual probabilities of getting 4, 5, 6, 7, 8, 9, and 10 Tails and sum them up.
To get the specific numerical values for each probability and the mean and standard deviation, you can plug in the values into the binomial distribution formula and calculate them using a calculator or statistical software.
I hope this helps! Let me know if you have any further questions.
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