概率：练习题

The probability of a fair six-sided die landing on a '4' is \( \frac{1}{6} \). If the die is rolled \( 120 \) times, what is the expected frequency of landing on a '4'?

A bag contains red, blue, and green counters. The probability of picking a red counter is \( 0.35 \) and the probability of picking a blue counter is \( 0.4 \). What is the probability of picking a counter that is not red or blue?

Events \( A \) and \( B \) are independent. Given that \( P(A) = 0.4 \) and \( P(B) = 0.5 \), calculate the probability \( P(A \cup B) \).<\/p>

Two fair spinners are spun. Spinner A has three sections labeled 1, 2, and 3. Spinner B also has three sections labeled 1, 2, and 3. The scores from the two spinners are added together. What is the probability that the sum of the scores is a prime number?<\/p>

Bag A contains \( 3 \) red balls and \( 7 \) blue balls. Bag B contains \( 5 \) red balls and \( 3 \) blue balls. A ball is chosen at random from Bag A and placed into Bag B. Then, a ball is chosen at random from Bag B. What is the probability that the ball chosen from Bag B is red?

A bag contains only red, blue, and yellow marbles. The probability of picking a red marble is 0.3 and the probability of picking a blue marble is 0.45.
Calculate the probability of picking a yellow marble.

Events \(A\) and \(B\) are mutually exclusive. Given that \(P(A) = 0.35\) and \(P(B) = 0.45\), calculate the probability \(P(A \cup B)\).

In a school of \(100\) students, \(65\) study French (\(F\)), \(40\) study German (\(G\)), and \(20\) study neither. A student is chosen at random from those who study French. Calculate the probability that this student also studies German.

A box contains red, blue, and green pens.
The probability of choosing a red pen is \(0.4\).
The probability of choosing a blue pen is \(0.35\).
(a) Calculate the probability of choosing a green pen.
(b) There are \(80\) pens in the box in total. Calculate the number of blue pens.
(c) If \(5\) additional red pens are added to the box, find the new probability of choosing a red pen. Give your answer as a fraction in its simplest form.

A bag contains 7 red counters and 5 blue counters. Two counters are taken from the bag at random, one after the other, without replacement.
(a) Draw a tree diagram or list the sample space to show all possible outcomes.
(b) Calculate the probability that both counters are of different colours.