Thuy rolls a number cube 7 times. Which expression represents the probability of rolling a 4 exactly 2 times? cap p times k successes is equal to n cap c sub k p to the k th power open paren 1 minus p close paren raised to the n minus k power n cap c sub k is equal to the fraction with numerator n factorial and denominator open paren n minus k close paren factorial times k factorial
Answer
A
7 cap c sub 2 2 sixths squared 4 sixths to the 5th power
B
7 cap c sub 5 1 sixth squared 1 sixth to the 5th power
C
7 cap c sub 5 1 sixth to the 5th power 5 sixths squared
D
7 cap c sub 2 1 sixth squared 5 sixths to the 5th power
Explanation
Use the binomial probability formula with 7 rolls, 2 successes, and probability 1/6 of rolling a 4 on each roll. The probability of not rolling a 4 is 5/6, so the expression is 7C2(1/6)^2(5/6)^5. This matches choice D.
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