Sec 2 Mathematics Probability of Single Events topical questions

A fair six-sided die is rolled once.

1. (a)Write the sample space.[1]
2. (b)Find P(prime number).[1]
3. (c)Find P(rolling a 7).[1]

A spinner has 8 equal sectors, of which 3 are shaded.

1. (a)Find P(shaded).[1]
2. (b)Find P(not shaded).[1]
3. (c)Write P(shaded) as a percentage.[1]

A bag holds 4 white and 6 black counters. One is drawn at random.

1. (a)Find P(white).[1]
2. (b)Find P(black).[1]
3. (c)Check that your two answers add up to 1, and explain why they must.[1]

A fair six-sided die is rolled once.

1. (a)Find P(a number greater than 4).[1]
2. (b)Find P(an odd number).[1]
3. (c)Find P(not rolling a 1).[1]

One letter is chosen at random from the word SINGAPORE.

1. (a)Find P(the letter S).[1]
2. (b)Find P(a vowel).[1]
3. (c)Find P(a consonant).[1]

One letter is chosen at random from the word PROBABILITY (11 letters).

1. (a)Find P(letter B).[1]
2. (b)Find P(vowel).[2]
3. (c)Find P(consonant).[1]

A card is drawn at random from cards numbered 1 to 20.

1. (a)Find P(multiple of 5).[2]
2. (b)Find P(factor of 6).[2]

A drawing pin is thrown 250 times. It lands point-up 140 times.

1. (a)Find the relative frequency of landing point-up.[2]
2. (b)Use it to estimate the chance the next throw lands point-up.[1]
3. (c)Explain why 0.5 is not a sensible theoretical answer here.[1]

About 12% of people are left-handed. A school has 400 pupils.

1. (a)How many left-handed pupils would you expect?[2]
2. (b)The school actually counts 52. Comment on this.[1]
3. (c)How many left-handed pupils would you expect in a class of 25?[1]

A bag holds 7 red, 5 blue and 8 green counters. One is drawn at random.

1. (a)Find P(green).[1]
2. (b)Find P(not red).[1]
3. (c)Find P(red or blue).[2]

A fair spinner shows the numbers 1 to 10, each equally likely.

1. (a)Find P(a multiple of 4).[1]
2. (b)Find P(a factor of 10).[1]
3. (c)Find P(neither a multiple of 4 nor a factor of 10).[2]

A fair die is rolled once.

1. (a)Find P(not a multiple of 3).[2]
2. (b)Find P(square number).[1]
3. (c)Find P(neither a multiple of 3 nor a square number).[2]

A coin is flipped 100 times and lands heads 62 times.

1. (a)Find the relative frequency of heads.[1]
2. (b)What relative frequency would a fair coin give in the long run?[1]
3. (c)Give one reason the coin might still be fair.[1]
4. (d)Describe what you would do to decide whether the coin is biased.[2]

A fair spinner shows the numbers 1 to 5, each equally likely.

1. (a)Find P(prime number).[1]
2. (b)Find P(not prime).[1]
3. (c)The spinner is spun 150 times. How many primes would you expect?[2]
4. (d)Give one reason an actual session might not produce exactly that number.[1]

A bakery loyalty card wins a free bun with probability 0.1 on each purchase. Mei makes 40 purchases in a year.

1. (a)How many free buns would you expect Mei to win?[1]
2. (b)Mei actually wins 7. Comment on this result.[2]
3. (c)How many purchases would give an expectation of 10 free buns?[1]
4. (d)Explain why the expectation is more trustworthy than one lucky streak.[1]