Determine the probability that a fish which is caught weighs less than 1.4 kg.

John catches 6 fish. Calculate the probability that at least 4 of the fish weigh more than 1.4 kg.

Determine the probability that a fish which is caught weighs less than 1 kg, given that it weighs less than 1.4 kg.

\({\text{P}}(x < 1.4) = 0.691\,\,\,\,\,\)(accept 0.692)     A1

[1 mark]

METHOD 1

\(y \sim {\text{B(6, 0.3085…)}}\)     (M1)

\({\text{P}}(Y \geqslant 4) = 1 - {\text{P}}(Y \leqslant 3)\)     (M1)

\( = 0.0775\,\,\,\,\,\)(accept 0.0778 if 3sf approximation from (a) used)     A1

METHOD 2

\(X \sim {\text{B(6, 0.6914…)}}\)     (M1)

\({\text{P}}(X \leqslant 2)\)     (M1)

\( = 0.0775\,\,\,\,\,\)(accept 0.0778 if 3sf approximation from (a) used)     A1

[3 marks]

\({\text{P}}(x < 1|x < 1.4) = \frac{{{\text{P}}(x < 1)}}{{{\text{P}}(x < 1.4)}}\)     M1

\( = \frac{{0.06680…}}{{0.6914…}}\)

\( = 0.0966\,\,\,\,\,\)(accept 0.0967)     A1

[2 marks]

Part (a) was almost universally correctly answered, albeit with an accuracy penalty in some cases. In (b) it was generally recognised that the distribution was binomial, but with some wavering about the correct value of the parameter p. Part (c) was sometimes answered correctly, but not with much confidence.

Part (a) was almost universally correctly answered, albeit with an accuracy penalty in some cases. In (b) it was generally recognised that the distribution was binomial, but with some wavering about the correct value of the parameter p. Part (c) was sometimes answered correctly, but not with much confidence.

Part (a) was almost universally correctly answered, albeit with an accuracy penalty in some cases. In (b) it was generally recognised that the distribution was binomial, but with some wavering about the correct value of the parameter p. Part (c) was sometimes answered correctly, but not with much confidence.