概率基礎與期望結果：練習題

A fair four-sided spinner is labelled \(1, 2, 3,\) and \(4\).
If the spinner is spun \(200\) times, how many times would you expect it to land on the number \(3\)?<\/p>

Two fair six-sided dice are rolled and their scores are added together.
What is the probability that the total score is exactly \(10\)? <\/p>

A box contains \(5\) red pens and \(3\) blue pens.
A pen is taken at random, the colour is recorded, and it is not replaced.
A second pen is then taken at random.
Calculate the probability that both pens are blue.<\/p>

A fair six-sided die is rolled once.
What is the probability of rolling an even number?

In a group of \(30\) people, \(18\) have a dog, \(12\) have a cat, and \(5\) have both a dog and a cat.
One person is chosen at random.
Given that the person has a dog, what is the probability that they also have a cat? <\/p>

A bag contains red, blue and green counters.
The probability of picking a red counter is \(0.3\).
The probability of picking a blue counter is \(0.4\).
Work out the probability of picking a green counter.

A bag contains only red, blue, and yellow counters.
The probability of picking a red counter is \( 0.35 \).
The probability of picking a blue counter is \( 0.2 \).
Calculate the probability of picking a yellow counter.

A bag contains 5 red balls and 3 blue balls. Two balls are taken at random from the bag without replacement.
Calculate the probability that the two balls are of different colours.

A company manufactures light bulbs and tests a sample of them for defects. The probability that a bulb is defective is \(0.04\).
(a) A worker picks two bulbs at random from the production line. Complete a tree diagram to show all possible outcomes and their probabilities.
(b) Calculate the probability that at least one of the two bulbs picked is defective.