Multiple Choice
Which of the following is true of the exponential smoothing coefficient in time series forecasting?
14
views
4. Probability
Basic Concepts of Probability
Struggling with Statistics?
Join thousands of students who trust us to help them ace their exams!Watch the first videoMultiple Choice
A fair coin is tossed times. What is the probability that at most tails occur?
A
B
C
D
Verified step by step guidance1
Recognize that the problem involves a binomial distribution because we have a fixed number of independent trials (28 coin tosses), each with two possible outcomes (heads or tails) and a constant probability of success (tail) of 0.5.
Define the random variable \(X\) as the number of tails in 28 tosses. Then, \(X\) follows a binomial distribution with parameters \(n = 28\) and \(p = \frac{1}{2}\).
The probability of getting exactly \(k\) tails is given by the binomial probability formula:
\[P(X = k) = \binom{28}{k} \left(\frac{1}{2}\right)^k \left(\frac{1}{2}\right)^{28 - k} = \binom{28}{k} \left(\frac{1}{2}\right)^{28}\]
To find the probability of getting at most 25 tails, sum the probabilities from \(k = 0\) to \(k = 25\):
\[P(X \leq 25) = \sum_{k=0}^{25} \binom{28}{k} \left(\frac{1}{2}\right)^{28}\]
Calculate or use statistical software or tables to evaluate the sum of these binomial probabilities to find the final probability.
5:37mWatch next
Master Introduction to Probability with a bite sized video explanation from Patrick
Start learningRelated Videos
Related Practice
Basic Concepts of Probability practice set
Problem sets built by lead tutorsExpert video explanations