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Paper 2 · Specimen 2026 · Statistical Tests and Distributions

The number of passes $X$ among $9$ students is modelled by $X \sim B(9, 0.4)$ . Find $P(X \ge 4)$ , to 3 decimal places.

Model answer

0.517

Also accepted: 0.5174, 0.52, 0.518

Explanation

Work with the complement:

P(X \ge 4) = 1 - P(X \le 3)

. Now

P(X=0) = 0.6^9 = 0.010078

,

P(X=1) = 9(0.4)(0.6)^8 = 0.060466

,

P(X=2) = 36(0.4)^2(0.6)^7 = 0.161243

and

P(X=3) = 84(0.4)^3(0.6)^6 = 0.250823

. These sum to

0.482610

, so

P(X \ge 4) = 0.51739

, that is

0.517

to 3 decimal places.

Derived from ZIMSEC Additional Mathematics Paper 2, Specimen Paper, Q7

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