Binomial distribution (Higher tier)：練習問題

Which of the following terms best describes the likelihood of an event that has a probability of 0.95 on the probability scale?

The probability of a student passing a math test is 0.75, and the probability of passing a science test is 0.80. Assuming these are independent events, calculate the probability that a student passes only one of the two tests.

Two groups, Group X and Group Y, are tested for a condition.
- In Group X, 5 out of 100 people have the condition.
- In Group Y, 15 out of 200 people have the condition.
Calculate the relative risk of having the condition in Group Y compared to Group X.

A fair six-sided die is rolled 120 times.
Calculate the expected frequency of rolling a 4.

In a town, the probability that a person has a specific allergy is 0.08. In a random sample of 1500 people, calculate the expected frequency of people who have this allergy.

A fair six-sided die is rolled 120 times.
Calculate the expected frequency of rolling a number greater than 4.

A factory inspector tests a batch of 500 light bulbs. The probability that a bulb is defective is 0.015<\/b>.
Calculate the expected frequency<\/b> of defective bulbs in this batch.<\/p>

Two events, \(A\) and \(B\), are such that \(P(A) = 0.6\), \(P(B) = 0.5\), and \(P(A \text{ and } B) = 0.2\).
Calculate the probability of \(P(A \text{ or } B)\)<\/b> and determine if events \(A\) and \(B\) are independent<\/b>. Justify your answer with a calculation.<\/p>

A fair six-sided die is rolled 120 times. The theoretical probability of rolling a '6' is \(\frac{1}{6}\).

A large sports club has 200 members. The following two-way table shows the number of members who play Tennis, Badminton, or both.