Probability Basics (Edexcel GCSE Statistics: Higher)

There are 13 coloured balls in container and 11 coloured balls in container .

In container , there are 4 orange balls and 9 white balls.
in container , there are 6 orange balls and 5 white balls.

Tanisha takes at random one ball from container and one ball from container .

Calculate the probability that the two balls selected by Tanisha are the same colour.

The Venn diagram shows probabilities relating to the three events , and .

Write down which two events from , and are mutually exclusive.
Give a reason for your answer.

Find

Find

Complete the Venn diagram below to show the probabilities relating to the two events and .

Humaira has a large box of dice.

She knows that 5 % of the dice in the box are biased.

All of the remaining dice are fair.

Humaira picks a dice at random, then replaces it in the box before picking a second dice at random from the same box.

She does not know if each dice she picked is biased or not.

Complete the probability tree diagram.

Show that the probability that both dice that Humaira picked were not biased is 0.9025.

Humaira claims that the probability that at least one of the dice she picked is not biased is greater than 98 %.

Determine whether or not Humaira is correct.

The director of a company that sells smartphones wants to investigate the selling of additional features. The additional features available are: premium insurance , cloud storage and screen protection .

Last week,

• 90 smartphones were sold

• 3 smartphones were sold with premium insurance, cloud storage and screen protection

• 8 smartphones were sold with cloud storage and screen protection only

• 2 smartphones were sold with premium insurance and screen protection only

• 11 smartphones were sold with premium insurance and cloud storage only

• 14 smartphones were sold with cloud storage only

• 52 smartphones in total were sold with screen protection

• 21 smartphones in total were sold with premium insurance

Complete the Venn diagram using this information.

Siobhan picks at random a smartphone that was sold last week.

She thinks that the probability the smartphone has screen protection given that it has cloud storage, is greater than the probability that the smartphone has screen protection given than it does not have cloud storage.

Is Siobhan correct?
You must show your working.

The company also sells smart TVs, both new and second-hand.

The company director records whether the smart TVs were new or second-hand and whether or not a fault with the TV was reported within 1 year after being sold.

The table gives information about the smart TVs sold by the company in January 2023.

Eric says that the relative risk of a second-hand smart TV developing a fault within 1 year of being sold, compared with a new smart TV developing a fault within 1 year of being sold, is 3

(i) Show that Eric is correct.

[2]

(ii) Interpret a relative risk of 3 in this context.

[1]

is the event that a student, in a particular school, studies French, where

is the event that a student, from the same school, studies Spanish, where

Some students at the school study both French and Spanish, where

A student is picked at random from the students at the school.

Work out .

A cinema sells three types of tickets: Adult tickets, Child tickets, and Student tickets. A ticket can be for an afternoon showing or an evening showing.

The incomplete two-way table gives some information about the number of each type of ticket sold last Sunday.

Complete the two-way table.

One of the people at the cinema for an evening showing is selected at random.

Write down the probability that they have a student ticket.

The manager of the cinema states that

"For afternoon showings, a higher proportion of tickets sold are for children than for evening showings"

Use data from the table to explain whether the manager is correct or not.

Abishek is investigating the types of devices that people use to access the internet on a regular basis.

Abishek asked 90 different people whether they used a desktop , a laptop or a smartphone to access the internet regularly.

The incomplete Venn diagram gives some information about Abishek's results.

One of the people that Abishek asked is chosen at random.

Given that, for this person,

complete the Venn diagram.

A manufacturer makes chairs and tables.

22 % of the items that are made by the company are tables.

5 % of the chairs made are found to not pass inspection.

11 % of the tables made are found to not pass inspection.

An item is to be picked at random.

Complete the probability tree diagram for this item.

One of the the items that is made by the manufacturer is picked at random.

is the event that the item is a chair.
is the event that the item passed the inspection.

Find .

and are two events such that

Genny says that

" and are independent events".

Do you agree?
Explain why.