Unit 7

Calculate the area of the shaded region, which consists of a semicircle with diameter 10 cm and a rectangle 10 cm by 6 cm. The diameter of the semicircle coincides with one side of the rectangle. Give your answer to 3 significant figures.

A solid has the same volume as a sphere with radius 2 cm. If the solid is a cube, what is the length of its side? Explain your steps.

In a survey of 60 students, 38 play football (F), and 15 play both football and tennis (T). A student is chosen at random. Calculate the probability that the student plays tennis given that they play football.

On a Venn diagram, set A represents people in a club who speak French, and set B represents those who speak Spanish. Out of 40 people, 18 speak French, 22 speak Spanish, and 9 speak both languages. Calculate how many people speak only Spanish.

Let and be sets in a universal set . Explain, using set notation, how to find the probability that an element chosen at random from lies in , and why you cannot simply add and unless and are disjoint.

In a group of 100 people, 65 like apples (A), 52 like bananas (B), and 29 like both apples and bananas.

54 children were surveyed about their favourite types of fruit. The Venn diagram below shows the number of children who like oranges (O), bananas (B), and apples (A).

Complete the table by finding the number of children who do not like any of these three fruits. Then, using the information, find the probability that a randomly selected child from this group likes at least two of the three fruits.

Let , , and the universal set . Write down the set and its number of elements.

In a set of 32 students, 18 study Physics (P), 15 study Chemistry (C), and 7 study both subjects. Work out the number of students who study either Physics or Chemistry, but not both.

A group of students was asked if they like music (M) and if they like art (A). Explain how you would use set notation and probability to work out the probability that a randomly selected student likes at least one of music or art, and the probability that a randomly selected student likes neither.