Probability: Practice Questions

A bag contains $$5$$ red balls and $$3$$ blue balls. A ball is chosen at random from the bag. What is the probability that the ball is blue?

A survey was conducted on 100 students to determine their preferred mode of transport to school. The results are summarized in the table below:

Gender vs Transport
| | Walk | Bus |
|---|---|---|
| Male | 20 | 30 |
| Female | 15 | 35 |

If a student is chosen at random from this group, find the probability that the student is female given that they walk to school.

The digits 1, 2, 3, 4, and 5 are arranged in a random order to form a five-digit number where no digit is repeated. Find the probability that the number formed is divisible by 4.

The probability of event A occurring is \( P(A) = 0.4 \) and the probability of event B occurring is \( P(B) = 0.3 \). If events A and B are mutually exclusive, find the probability that either A or B occurs, \( P(A \text{ or } B) \).

A box contains 10 good items and 3 defective items. If 4 items are selected at random without replacement, what is the probability that at least 2 of them are good?

In a school, $$60\%$$ of students study Mathematics and $$45\%$$ study Physics. If $$20\%$$ of students study both Mathematics and Physics, find the probability that a randomly chosen student studies neither Mathematics nor Physics.

Three independent events A, B, and C have probabilities \(P(A) = 0.3\), \(P(B) = 0.5\), and \(P(C) = 0.2\). Find the probability that at least one of the events occurs.