Probability basics and expected outcomes：練習問題

The probability that a biased seed germinates is \(0.85\).
A gardener plants \(300\) of these seeds.
Work out the expected number of seeds that will germinate.

There are \(18\) pens in a drawer.
\(11\) pens are blue and \(7\) pens are black.
Two pens are taken at random from the drawer without replacement.
Work out the probability that both pens are blue.

There are \(50\) members in a sports club.
\(32\) members play tennis.
\(22\) members play squash.
\(8\) members play neither tennis nor squash.
A member who plays tennis is selected at random.
Work out the probability that this member also plays squash.

A biased spinner can land on Red, Blue, or Green. The probability of landing on Red is \( 0.4 \). The probability of landing on Blue is \( 0.35 \).
What is the probability of landing on Green?

In a class of \(30\) students, \(18\) study French, \(15\) study German, and \(7\) study both languages.
A student is chosen at random from the class.
Work out the probability that the student studies neither French nor German.

A letter is chosen at random from the word MATHEMATICS.
Work out the probability that the letter is an M.
Give your answer as a fraction in its simplest form.

In a group of \(40\) students, \(22\) study French, \(18\) study Spanish, and \(6\) study neither.
A student is picked at random from the group.
Work out the probability that the student studies both French and Spanish.

The Venn diagram shows the number of elements in sets \(A\) and \(B\) within a universal set \(\xi\):

A student is selected at random from the group.
Given that the student is in set \(A\), work out the probability that the student is also in set \(B\).
Give your answer as a fraction in its simplest form.

A fair four-sided spinner is spun once.
The sides of the spinner are labelled \(2\), \(4\), \(6\), and \(8\).
A fair coin is flipped once with possible outcomes Heads (\(H\)) and Tails (\(T\)).

(a) List all the possible paired outcomes of spinning the spinner and flipping the coin.
(b) Work out the probability of obtaining an outcome with a number greater than \(5\) and Tails (\(T\)). Give your answer as a fraction in its simplest form.

In a school of \(100\) students, \(65\) study French, \(45\) study German, and \(20\) study neither language.

(a) Complete the analysis to work out the number of students who study both French and German.
(b) A student is selected at random from those who study French. Work out the probability that this student also studies German.
Give your answer as a fraction in its simplest form.