(a) Two ponds, A and B, each contain a large number of fish. It is known that 2.4% of fish in pond A
are carp and 1.8% of fish in pond B are carp. Random samples of 50 fish from pond A and 60 fish
from pond B are selected.
Use appropriate Poisson approximations to find the following probabilities.
(i) The samples contain at least 2 carp from pond A and at least 2 carp from pond B.
(ii) The samples contain at least 4 carp altogether.
(b) The random variables X and Y have the distributions Po(λ) and Po(μ) respectively. It is given
that
• P(X = 0) = [P(Y = 0)]²,
• P(X = 2) = k[P(Y = 1)]², where k is a non-zero constant.
Find the value of k.

Q: What topic does this question test?

This question tests Probability and statistics in A-Level Mathematics (syllabus code 9709). It is worth 10 marks.

Q: Which exam paper is this question from?

This question appeared in the Cambridge A-Level Mathematics Feb/Mar 2022 examination, Paper 6 Variant 2 (9709_m22_qp_62.pdf).

Question

(a) Two ponds, A and B, each contain a large number of fish. It is known that 2.4% of fish in pond A
are carp and 1.8% of fish in pond B are carp. Random samples of 50 fish from pond A and 60 fish
from pond B are selected.
Use appropriate Poisson approximations to find the following probabilities.
(i) The samples contain at least 2 carp from pond A and at least 2 carp from pond B.
(ii) The samples contain at least 4 carp altogether.
(b) The random variables X and Y have the distributions Po(λ) and Po(μ) respectively. It is given
that
• P(X = 0) = [P(Y = 0)]²,
• P(X = 2) = k[P(Y = 1)]², where k is a non-zero constant.
Find the value of k.

Oracle Prep · Accepted Answer

Sign up to Oracle Prep to view the full model answer with examiner insights.

📋 Examiner Report & Trap Analysis

🎯 Mark Scheme Breakdown

Unlock the Examiner's Analysis

About This A-Level Mathematics Question

Topic

Source

Practice on Oracle Prep

Related Mathematics Questions