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Probabilities from frequency tables

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Probability of event for KS4

1. Definition of event probability

1.1. Statistical definition of probability

1.2. Classical definition of probability

2. Event Probability Properties

2.1. Derivation of the equation of the classical definition of probability

3. Axiomatic definition of probability

4. Forum

↓ Show theory [1] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:probabilities_from_frequency_tables/5296/

Example 1.

Jack wanted to know if taking coffee at night could really help him sleep less and study more. For several nights, Jack recorded how many cups of coffee he drank at night and how many hours he slept that night.

	6 hours	7 hours
0 cup of coffee	6	4
1 cup of coffee	5	2

What is the probability that a randomly selected night is one when he drank exactly 1 cup of coffee and is one when he slept exactly 6 hours?

the problem is without solution steps

Example 2.

	6 hours	7 hours
0 cup of coffee	6	4
1 cup of coffee	5	2

If a night is chosen at random, what is the probability that it's a night when Jack took no coffee and slept for 7 hours?

the problem is without solution steps

	6 hours	7 hours
0 cup of coffee	6	4
1 cup of coffee	5	2

If a night is chosen at random, what is the probability that it's a night when Jack slept for 7 hours?

the problem is without solution steps

Alice is a teacher and a sandwich maker. Last month, she tracked the number of peanut butter and jam sandwiches her students brought to school, noting the flavour of jam and the type of peanut butter.

	Creamy peanut butter	Chunky peanut butter
Strawberry jam	2	3
Grape jam	6	2

What is the probability that a randomly selected sandwich was made with grape jam and creamy peanut butter?

the problem is without solution steps

	Creamy peanut butter	Chunky peanut butter
Strawberry jam	2	3
Grape jam	6	2

If a sandwich is randomly selected, what is the probability that it is made with strawberry jam and chunky peanut butter?

the problem is without solution steps

	Creamy peanut butter	Chunky peanut butter
Strawberry jam	2	3
Grape jam	6	2

If a sandwich is randomly selected, what is the probability that it is made with chunky peanut butter?

the problem is without solution steps

Parker, being the manager of a company, is served a cup of coffee by her secretary every morning. For some days, Parker counted all the teacups used to serve him coffee, noting their colours and size.

	Small	Medium
Green	4	2
Yellow	2	3

What is the probability that a randomly selected cup is yellow and small?

the problem is without solution steps

	Small	Medium
Green	4	2
Yellow	2	3

If a cup is chosen at random, what is the probability that it is yellow and a medium size?

the problem is without solution steps

	Small	Medium
Green	4	2
Yellow	2	3

What is the probability that a randomly selected cup is small or yellow?

the problem is without solution steps

10.

Tina watched different football matches between teams A and B in which team A celebrated victory times. Calculate the relative frequency of Team A's victory. By how much does the relative frequency differ from the theoretical probability of the event? Express the result as a percentage .