Aron flips a penny 9 times. Which expression represents the probability of getting exactly 3 heads? 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 k factorial
Answer
A
9 cap c sub 3 0 point 5 cubed 0 point 5 to the 6th power
B
9 cap c sub 6 0 point 5 to the 6th power
C
9 cap c sub 3 0 point 5 cubed 0 point 5 to the 9th power
D
9 cap c sub 3 0 point 5 cubed
Explanation
Use the binomial probability formula with 9 flips, 3 successes (heads), and a head probability of 0.5. This gives 9C3(0.5)^3(1 − 0.5)^(9−3), or 9C3(0.5)^3(0.5)^6. Choice A has this expression.
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