\( (-4,3) \) 0.16 0.12 0.03 4. Choose the correct answer. You have a multiple-choice test of 25 questions with 4 choices for each question. You choose each answer at random and get 4 answers correct. What is the probabilit 0.04

To find the probability of getting 4 correct answers out of 25 questions, we can use the binomial probability formula. The binomial probability formula is given by: \[ P(X = k) = \binom{n}{k} \times p^k \times (1-p)^{n-k} \] Where: - \( n \) is the total number of trials (questions in this case), - \( k \) is the number of successful trials (correct answers), - \( p \) is the probability of success (getting a correct answer) on a single trial. In this case, we have: - \( n = 25 \) (total number of questions), - \( k = 4 \) (number of correct answers), - \( p = 0.04 \) (probability of getting a correct answer). Substitute these values into the binomial probability formula to find the probability of getting 4 correct answers out of 25 questions. Simplify the expression by following steps: - step0: Solution: \(25cho\times ose\times 4\times 0.04^{4}\left(1-0.04\right)^{21}\) - step1: Subtract the numbers: \(25cho\times ose\times 4\times 0.04^{4}\times 0.96^{21}\) - step2: Convert the expressions: \(25cho\times ose\times 4\left(\frac{1}{25}\right)^{4}\times 0.96^{21}\) - step3: Convert the expressions: \(25cho\times ose\times 4\left(\frac{1}{25}\right)^{4}\left(\frac{24}{25}\right)^{21}\) - step4: Transform the expression: \(25cho\times ose\times 4\times 25^{-4}\left(\frac{24}{25}\right)^{21}\) - step5: Multiply the terms: \(25^{1-4}cho\times ose\times 4\left(\frac{24}{25}\right)^{21}\) - step6: Subtract the numbers: \(25^{-3}cho\times ose\times 4\left(\frac{24}{25}\right)^{21}\) - step7: Multiply the terms: \(25^{-3}cho^{2}se\times 4\left(\frac{24}{25}\right)^{21}\) - step8: Multiply the terms: \(\frac{ch}{25^{3}}\times o^{2}se\times 4\left(\frac{24}{25}\right)^{21}\) - step9: Multiply the terms: \(\frac{cho^{2}}{25^{3}}\times se\times 4\left(\frac{24}{25}\right)^{21}\) - step10: Multiply the terms: \(\frac{cho^{2}s}{25^{3}}\times e\times 4\left(\frac{24}{25}\right)^{21}\) - step11: Multiply the terms: \(\frac{echo^{2}s}{25^{3}}\times 4\left(\frac{24}{25}\right)^{21}\) - step12: Multiply the terms: \(\frac{4echo^{2}s}{25^{3}}\times \left(\frac{24}{25}\right)^{21}\) - step13: Rewrite the expression: \(\frac{4echo^{2}s}{25^{3}}\times \frac{24^{21}}{25^{21}}\) - step14: Multiply the terms: \(\frac{4echo^{2}s\times 24^{21}}{25^{3}\times 25^{21}}\) - step15: Multiply the terms: \(\frac{4\times 24^{21}echo^{2}s}{25^{3}\times 25^{21}}\) - step16: Multiply the terms: \(\frac{4\times 24^{21}echo^{2}s}{25^{24}}\) The probability of getting 4 correct answers out of 25 questions is \( \frac{4 \times 24^{21} \times 0.04^2}{25^{24}} \).