Pancyprian Examinations (Cyprus) · Mathematics

Probability

10 practice questions, each with the answer and an explanation.

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For events $A$ and $B$ : $P (A) = 0.5$ , $P (B) = 0.3$ and $P (A \cup B) = 0.65$ . What is $P (A \cap B)$ , and are $A$ and $B$ independent?
In a school, $60%$ of the students have a laptop and $25%$ have both a laptop and a tablet. A student with a laptop is chosen. What is the probability that the student also has a tablet?
A bag holds $5$ red and $3$ green balls. Two balls are drawn without replacement. What is the probability that they have the same colour?
A fair coin is tossed $4$ times. What is the probability of at least one head?
Two fair dice are rolled. What is the probability that the sum is at least $10$ ?
Events $A$ and $B$ are mutually exclusive with $P (A) = 0.3$ and $P (B) = 0.45$ . What is $P (A \cup B)$ ?
Events $A$ and $B$ are independent with $P (A) = 0.4$ and $P (B) = 0.5$ . What is $P (A \cup B)$ ?
Machine A makes $60%$ of a factory's items, of which $2%$ are defective. Machine B makes the other $40%$ , of which $5%$ are defective. What is the probability that a randomly chosen item is defect…
For the factory above, $P (defective) = 0.032$ and $P (from B and defective) = 0.020$ . A defective item is found. What is the probability it came from machine B?
An integer is chosen at random from $1$ to $30$ . What is the probability that it is a multiple of $3$ or a multiple of $5$ ?

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