1.A balanced coin is tossed 8 times. Let X denotes the number of heads. Calculate the following: / ‘n Gebalanseerde muntstuk word 8 keer gewerp. Laat X die aantal munte aandui. Bereken die volgende:
1.1P(X = 5)
1.2P(X 2)
1.3P(X > 2)
1.1 P(X = 5) = (8 choose 5) * (0.5)^5 * (0.5)^(8-5) = 56 * 0.03125 * 0.125 = 0.21875
1.2 P(X ≥ 2) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)
= (8 choose 2) * (0.5)^2 * (0.5)^(8-2) + (8 choose 3) * (0.5)^3 * (0.5)^(8-3) + (8 choose 4) * (0.5)^4 * (0.5)^(8-4) + 0.21875 + (8 choose 6) * (0.5)^6 * (0.5)^(8-6) + (8 choose 7) * (0.5)^7 * (0.5)^(8-7) + (0.5)^8 = 0.890625
1.3 P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)
= (8 choose 3) * (0.5)^3 * (0.5)^(8-3) + (8 choose 4) * (0.5)^4 * (0.5)^(8-4) + 0.21875 + (8 choose 6) * (0.5)^6 * (0.5)^(8-6) + (8 choose 7) * (0.5)^7 * (0.5)^(8-7) + (0.5)^8 = 0.765625