5. Labrador puppies may be black, yellow or chocolate in colour. Some information about a litter of 9 puppies is given in the table. Four puppies are chosen at random to train as guide dogs.
(b) Determine the probability that at least 3 black puppies are chosen.
(c) Determine the probability that exactly 3 females are chosen given that at least 3 black puppies are chosen.
(d) Explain whether the 2 events
'choosing exactly 3 females' and 'choosing at least 3 black puppies' are independent events. A firm claims that no more than \(2 \%\) of their packets of sugar are underweight. A market researcher believes that the actual proportion is greater than \(2 \%\). In order to test the firm's claim, the researcher weighs a random sample of 600 packets and carries out a hypothesis test, at the \(5 \%\) significance level, using the null hypothesis \(p = 0.02\).
(a) Given that the researcher's null hypothesis is correct, determine the probability that the researcher will conclude that the firm's claim is incorrect.
(b) The researcher finds that 18 out of the 600 packets are underweight. A colleague says
" 18 out of 600 is \(3 \%\), so there is evidence that the actual proportion of underweight bags is greater than \(2 \%\)." Criticise this statement.