8.02 Conditional probability

Find P \left( B|A \right) given the following probabilities for an experiment in which A and B are two possible events:

A basketball team has a probability of 0.8 of winning its first season and 0.15 of winning its first season and its second season. Find the probability of winning the second season, given they won first.

In a population, 35\% of people have brown eyes, 45\% of people have blonde hair, and 10\% of people have both brown eyes and blonde hair. A person is chosen randomly from the population. Find the probability that they have:

Find P \left( A \cap B \right) given the following probabilities for an experiment in which A and B are two possible events:

The probability of two independent events, A and B are P \left( A \right) = 0.6 and P \left( B \right) = 0.7. Determine the probability of:

Amelia has 4 cards, each with one of the following numbers printed on it: 2, 9, 1, 7

A student is choosing 2 units to study at university: a language and a science unit. They have 5 languages and 8 science units to choose from.

For breakfast each morning, Marge eats porridge, toast or cereal. With that she will either drink orange juice, tea or hot chocolate. Find the probability that Marge will:

A netball coach is choosing players for the Goal Keeper and Goal Defence positions out of the following people:

• Goal Keeper position: Beth, Amy, Joy, Tara.

• Goal Defence position: Eve, Cara, Daisy, Kim, Liz.

The selection for each position is made independently.

Two dice are rolled, one after another. Find the probability, in simplest form, of rolling:

A card is randomly drawn from a standard 52 pack of cards. Find the probability that it's a jack, queen, king or ace if:

Four identical balls labelled 1, 2, 3 and 4 are in a bag. Two balls are randomly drawn from the bag in succession and without replacement. Find the probability, in simplest form, that:

Two cards are randomly drawn without replacement from a deck of cards numbered from 1 to 20. Find the probability that the second card is:

A flight departs from Melbourne to Sydney. The following probabilities were found with regard to departure times and weather:

• The probability that the flight departs on time, given the weather is fine in Melbourne is 0.9.

• The probability that the flight departs on time, given the weather is not fine in Melbourne is 0.7.

• The probability that the weather is fine on any particular day in July is 0.4.

Find the probability that:

A museum has new software to determine whether a painting is fake or authentic. The system has an accuracy of 75\%. Art experts have previously determined that 5\% of paintings that the museum examines are fakes.

Find the probability that:

There are two positions available at a company and the applicants have been shortlisted down to 6: Patricia, Nadia, Amy, Aaron, Lachlan, Jimmy. The two people to fill the position will be picked randomly.

Two sets of numbers, A and B, are such that set A contains the even numbers from 1 to 20, inclusive, and set B contains the factors of 48 from 1 to 20, inclusive.

Harry is struggling to decide what movie to watch. He decides to pick one at random from his collection. A Venn diagram of his collection sorts movies into three categories:

a

How many movies are there in Harry's collection?

b

Harry wants to watch a comedy. Find the probability he will select a a comedy.

c

Harry is after a film that goes for longer than 2 hours. Find the probability that he will select a suitable film given that he chooses a comedy.

d

Harry is after a film that goes for less than 2 hours. Find the probability that he will select a suitable film given that he selects a romantic comedy.

A group of people were asked what type of exercise they like to do. The results are shown in the Venn diagram below:

A person is chosen from the group at ramdom.

a

Find the probability that the person walks.

b

Find the probability that the person runs, given that they also walk.

At a university there are 816 students studying first year engineering, 497 of whom are female (set F). Of the 348 students studying Civil Engineering (set C), 237 of them are women.

a

Find the value of:

i

w

ii

x

iii

y

iv

z

b

Find the probability that a randomly selected male student does not study Civil Engineering.

Neil watches three episodes of TV each night. He begins with News or Current Affairs, then the next two shows are either Comedy, Horror or Animation. He never watches more than one Horror show, and if he watched the News, he will follow this immediately with a Comedy.

When Fred gets ready for work in summer, he first decides whether it will be a hot day (H) or not (N) and then decides whether to wear a tie (T) or to just dress casually (C).

\\

The chance of Fred deciding it will be a hot day is 0.7. If he decides it will be a hot day, there is a 0.2 chance he will wear a tie. If he decides it will not be a hot day, there is a 0.85 chance he will wear a tie.

A player is rolling 2 dice and looking at their difference, that is, the largest number minus the smaller number. They draw up a table of all the possible dice rolls for 2 dice and what their difference is:

In a survey, 151 children were asked whether they had read or watched at least one of the stories in the Harry Potter series.

• 60 hadn’t read any of the books

• 33 had read and watched at least one of the stories

• 85 had watched the movie,

• 8 had never read or watched any of these

Two hundred people were questioned about whether they voted for Labor, Liberal or Greens last election and who they’ll vote for this election.