Example Question - probability of success
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Calculating Number of Trials in Binomial Test with Probability 1/2
The question provided in the image asks to find the value of \( n \) in a binomial test where \( p = 1/2 \), \( p \cdot n = 35 \), and \( q \cdot n = 35 \) as well. Here, \( p \) is the probability of success on a single trial, \( q \) is the probability of failure on a single trial, and \( n \) is the number of trials. Since \( p = 1/2 \), this means that \( q \), the probability of failure, must also be equal to \( 1/2 \) since \( p + q = 1 \). Given \( p \cdot n = 35 \), and we know \( p = 1/2 \), we can solve for \( n \) as follows: \[ 1/2 \cdot n = 35 \] Now, to find \( n \), we multiply both sides of the equation by 2: \[ n = 2 \cdot 35 \] \[ n = 70 \] Therefore, \( n \), the number of trials, is 70.
Solving for n in a Binomial Test
The image presents a question related to a binomial test: For a binomial test, if p = 1/2, p*n = 35 and q*n = 35, what is the value of n? Here, p is the probability of success on a single trial, and q is the probability of failure (q = 1 - p). Since we know p, we can find q: q = 1 - p = 1 - 1/2 = 1/2 With the formulas p*n and q*n equaling 35, we have: p*n = 35 q*n = 35 Since both p and q are equal to 1/2, and both p*n and q*n are equal to 35, we can solve for n: (1/2)*n = 35 n = 35 / (1/2) n = 35 * 2 n = 70 Thus, the value of n is 70.
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