ESAT (Engineering and Science Admissions Test) · Mathematics 1

Probability

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

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 7 questions

For events $A$ and $B$ , $P (A) = 0.5$ , $P (B) = 0.4$ and $P (A \cup B) = 0.7$ . What is $P (A ∣ B)$ ?
In a class of $60$ students, $35$ like maths, $25$ like physics and $15$ like both. A student who likes physics is chosen. What is the probability that this student also likes maths?
The probability of rain is $0.3$ . If it rains, the chance a bus is late is $0.4$ ; if it does not rain, the chance is $0.1$ . What is the probability that the bus is not late?
A bag holds $5$ red and $3$ blue counters. Two counters are drawn at random without replacement. What is the probability that both are red?
A fair six-sided die is rolled three times. What is the probability of getting at least one six?
A game costs $£2$ to play. A fair die is rolled: a $6$ pays $£6$ , a $4$ or $5$ pays $£1$ , and anything else pays nothing. What is the expected net result per game?
In how many different ways can the letters of the word LEVEL be arranged?

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