Research has shown that studying improves a student's chances to 80 % of selecting the correct answer to a multiple choice question. A multiple choice test has 15 questions. Each question has 4 choices and exactly one is correct. Probability that the student does exactly 7 or 8 correct answer when he studies and attempts all the questions.

Question

Research has shown that studying improves a student's chances to 80 % of selecting the correct answer to a multiple choice question. A multiple choice test has 15 questions. Each question has 4 choices and exactly one is correct. Probability that the student does exactly 7 or 8 correct answer when he studies and attempts all the questions. (A)  15 C 7 ⋅((4/5))7 ⋅((1/5))8 (B)  15 C7 ⋅((4/5))8 ⋅((1/5))7 (C)  15 C7 ⋅((4/5))7 ⋅((1/5))7 (D) can't be determined

Tardigrade Admin · Accepted Answer

Correct answer is (c) 15 C7 ⋅((4/5))7 ⋅((1/5))7

$^{15} C_{7} \cdot (\frac{4}{5})^{7} \cdot (\frac{1}{5})^{8}$

$^{15} C_{7} \cdot (\frac{4}{5})^{8} \cdot (\frac{1}{5})^{7}$

$^{15} C_{7} \cdot (\frac{4}{5})^{7} \cdot (\frac{1}{5})^{7}$

can't be determined

Correct answer is (c) $^{15} C_{7} \cdot (\frac{4}{5})^{7} \cdot (\frac{1}{5})^{7}$

15C7​⋅(54​)7⋅(51​)8

15C7​⋅(54​)8⋅(51​)7

15C7​⋅(54​)7⋅(51​)7

can't be determined

Correct answer is (c) 15C7​⋅(54​)7⋅(51​)7

$^{15} C_{7} \cdot (\frac{4}{5})^{7} \cdot (\frac{1}{5})^{8}$

$^{15} C_{7} \cdot (\frac{4}{5})^{8} \cdot (\frac{1}{5})^{7}$

$^{15} C_{7} \cdot (\frac{4}{5})^{7} \cdot (\frac{1}{5})^{7}$

Correct answer is (c) $^{15} C_{7} \cdot (\frac{4}{5})^{7} \cdot (\frac{1}{5})^{7}$