Assume that the playbook contains 16 passing plays and 9 running plays. The coach randomly selects 9 plays from the playbook.

Question

 Assume that the playbook contains 16 passing plays and 9 running plays. The coach randomly selects 9 plays from the playbook.

What is the probability that the coach selects at least 3 passing plays and at least 3 running plays? 

Answer 1

 Assume that the playbook contains 16 passing plays and 9 running plays. The coach randomly selects 9 plays from the playbook.

What is the probability that the coach selects at least 3 passing plays and at least 3 running plays? 

= P(3Run) P(6pass) + P(4Run) P(5pass) + P(5run) P(4pass) + P(6run) P(3pass)

= [ ₁₆C₃ * ₉C₆ + ₁₆C₄ * ₉C₅ + ₁₆C₅ * ₉C₄ + ₁₆C₆ * ₉C₃ ] / ₂₅C₉

_{= ( 560 * 84 + 1820 * 126 + 4368 * 126 + 8008 * 84 ) / 2042975}

_{= ( 47040 + 229320 + 550368 + 672672 ) / 2042975}

_{= 1499407 / 2042975}

_{= 0.7339}

_{or 73.4%}