P(X=10) = C(10,10) (0.8)^10 = 1 × 0.1073741824 ≈ 0.10737

February 22, 2026

P(X=10) = C(10,10) (0.8)^10 = 1 × 0.1073741824 ≈ 0.10737

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P(X=k) = C(10,k) (0.8)^k (0.2)^(10−k)
P(X=8) = C(10,8) (0.8)^8 (0.2)^2 = 45 × 0.16777216 × 0.04 ≈ 0.30199
P(X=9) = C(10,9) (0.8)^9 (0.2)^1 = 10 × 0.134217728 × 0.2 ≈ 0.268435
Sum ≈ 0.30199 + 0.268435 + 0.10737 = <<0.30199+0.268435+0.10737=0.677795>>0.6778 (rounded to 4 decimal places)
#### 0.6778
An ornithologist observes that a flock of birds increases its daily migration distance by 12% each day during a 5-day journey. If they fly 40 km on the first day, what is the total distance flown over the 5 days?

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