\( \left. \begin{array} { l } { \left. \begin{array} { l } { P ( t ) } \\ { n = 26 } \\ { x = 14 } \\ { p = 0,6 } \end{array} \right. \quad P ( x ) = \left( \begin{array} { l } { n } \\ { x } \end{array} \right) p ^ { x } ( 1 - p ) ^ { n - x } } \\ { } \end{array} \right. \)

It looks like you're working with a binomial probability formula. The formula for the probability of getting exactly \( x \) successes in \( n \) independent Bernoulli trials (where each trial has a success probability of \( p \)) is given by: \[ P(x) = \binom{n}{x} p^x (1 - p)^{n - x} \] Where: - \( \binom{n}{x} \) is the binomial coefficient, calculated as \( \frac{n!}{x!(n-x)!} \). - \( n \) is the total number of trials. - \( x \) is the number of successes. - \( p \) is the probability of success on an individual trial. In your case, you have: - \( n = 26 \) - \( x = 14 \) - \( p = 0.6 \) Now, let's calculate \( P(14) \): 1. Calculate the binomial coefficient \( \binom{26}{14} \): \[ \binom{26}{14} = \frac{26!}{14!(26-14)!} = \frac{26!}{14! \cdot 12!} \] 2. Calculate \( p^x \) and \( (1 - p)^{n - x} \): \[ p^x = 0.6^{14} \] \[ (1 - p)^{n - x} = (0.4)^{12} \] 3. Combine these values to find \( P(14) \): \[ P(14) = \binom{26}{14} \cdot 0.6^{14} \cdot 0.4^{12} \] Now, let's compute these values step by step. ### Step 1: Calculate the binomial coefficient Using a calculator or software to compute \( \binom{26}{14} \): \[ \binom{26}{14} = 10400600 \] ### Step 2: Calculate \( 0.6^{14} \) and \( 0.4^{12} \) Using a calculator: \[ 0.6^{14} \approx 0.0060466176 \] \[ 0.4^{12} \approx 0.00016777216 \] ### Step 3: Combine the results Now, plug these values into the formula: \[ P(14) = 10400600 \cdot 0.0060466176 \cdot 0.00016777216 \] Calculating this gives: \[ P(14) \approx 0.104 \] Thus, the probability of getting exactly 14 successes in 26 trials with a success probability of 0.6 is approximately \( 0.104 \) or \( 10.4\% \).