ECZ 2025 · GCE Paper 2 · Question 3 — Matrices

Matrix P = 4-211. A box contains 6 white circuit breakers and 4 black circuit breakers, all identical in appearance. A circuit breaker is selected at random and not replaced. A second is then selected.

(a(i)) Find the determinant of matrix P.[2]

Verified working — step 1

P = matrix(…

(a(ii)) Find the inverse of matrix P.[2]

Verified working — step 1

For P = abcd, P^-1 = (1det)d-b-ca

(b(i)) Find the probability that both circuit breakers selected are white.[2]

Verified working — step 1

Total breakers = 6 white + 4 black = 10

(b(ii)) Find the probability that the circuit breakers selected are of different colours.[3]

Verified working — step 1

P(different colours) = P(W then B) + P(B then W)

The full step-by-step working and final answer are included with Premium — checked against ECZ marking standards.

Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

Have a different question?

Search it — if it is from a past paper or a school mock, chances are we have it worked out, or one that uses the same method.