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Shaquille O’ Neal is a $60\%$ career free throw shooter, meaning that he successfully makes $60$ free throws out of $100$ attempts on average. What is the probability that he will successfully make exactly $6$ free throws in $10$ attempts?

  1. $0.2508$
  2. $0.2816$
  3. $0.2934$
  4. $0.6000$
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Let $p$ be the probability of success cases and $q$ be the probability of failure cases.

Given, $p = 0.6, q = 0.4$

The probability of $6$ successful throws out of $10$ can be given as:

$=\ ^{10}C_6p^6q^{10-6}\\=\ ^{10}C_6(0.6)^6(0.4)^4\\ =\ 210 \times 0.046656 \times 0.0256\\ =\ 0.2508$

Correct Answer: $A$
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