a) the coin lands tails exactly 7 times b)the coin lands tails at least 11 times c)the coin lands tails at most 3 times Solution a) The coin lands tails exactly 7 times. a) P(7) = (½)^14 •14C7 ˜ .21 b) The coin lands tails at least 11 times. b) P(=11 = P(11) + P(12) + P(13) + P(14) = (½)^14 •14C11 + (½)^14 •14C12 + (½)^14 •14C13 + (½)^14 •14C14 = (½)^14 •(14C11 + 14C12 + 14C13 + 14C14) = (½)^14 •(364 + 91 + 14 + 1) = (½)^14 •(470) ˜ 0.029 P(=11) ˜ 0.029 c) The coin lands tails at most 3 times. c) P(=3) = P(0) + P(1) + P(2) + P(3) ˜ 0.029 continue to see why (½)^14 •14C0 + (½)^14 •14C1 + (½)^14 •14C2 + (½)^14 •14C3 = (½)^14 •(14C0 +14C1 +14C2 +14C3) = (½)^14 •(1 + 14 + 91 +364) = (½)^14 •(470) ˜ 0.029 P(=3) ˜ 0.029.