Incomplete two-way table completion

2 When Joanna cooks, the probability that the meal is served on time is \(\frac { 1 } { 5 }\). The probability that the kitchen is left in a mess is \(\frac { 3 } { 5 }\). The probability that the meal is not served on time and the kitchen is not left in a mess is \(\frac { 3 } { 10 }\). Some of this information is shown in the following table.

1. Copy and complete the table.
2. Given that the kitchen is left in a mess, find the probability that the meal is not served on time.

7. In a large college, \(\frac { 3 } { 5 }\) of the students are male, \(\frac { 3 } { 10 }\) of the students are left handed and \(\frac { 1 } { 5 }\) of the male students are left handed. A student is chosen at random.

1. Given that the student is left handed, find the probability that the student is male.
2. Given that the student is female, find the probability that she is left handed.
3. Find the probability that the randomly chosen student is male and right handed. Two students are chosen at random.
4. Find the probability that one student is left handed and one is right handed.

15 A sample of 200 households was obtained from a small town.
Each household was asked to complete a questionnaire about their purchases of takeaway food.
\(A\) is the event that a household regularly purchases Indian takeaway food.
\(B\) is the event that a household regularly purchases Chinese takeaway food.
It was observed that \(\mathrm { P } ( B \mid A ) = 0.25\) and \(\mathrm { P } ( A \mid B ) = 0.1\)
Of these households, 122 indicated that they did not regularly purchase Indian or Chinese takeaway food.
A household is selected at random from those in the sample.
Find the probability that the household regularly purchases both Indian and Chinese takeaway food.
[0pt] [6 marks]

7. In a school there are 148 students in Years 12 and 13 studying Science, Humanities or Arts subjects. Of these students, 89 wear glasses and the others do not. There are 30 Science students of whom 18 wear glasses. The corresponding figures for the Humanities students are 68 and 44 respectively. A student is chosen at random. Find the probability that this student

1. is studying Arts subjects,
2. does not wear glasses, given that the student is studying Arts subjects. Amongst the Science students, \(80 \%\) are right-handed. Corresponding percentages for Humanities and Arts students are 75\% and 70\% respectively. A student is again chosen at random.
3. Find the probability that this student is right-handed.
4. Given that this student is right-handed, find the probability that the student is studying Science subjects.

1. Joel buys a box of second-hand Jazz and Blues CDs at a car boot sale.

In the box there are 30 CDs, 8 of which were recorded live. 16 of the CDs are predominantly Jazz and 13 of these were recorded in the studio. This information is shown in the following table.

1. Copy and complete the table above. Joel picks a CD at random to play first.
   Find the probability that it is
2. a Blues CD that was recorded live,
3. a Jazz CD, given that it was recorded in the studio.