Remember when you thought all those hypothetical maths problems in school would never come up again in real life? Well, here they are.
There are four numbers less than five (1, 2, 3, 4) and six total possible outcomes (1, 2, 3, 4, 5, 6) so the answer is 4/6.
There are three even numbers (2, 4, 6) and six total possible outcomes (1, 2, 3, 4, 5, 6) so the answer is 3/6, which can be simplified to 1/2.
There are 52 playing cards in total in a pack, and four of them are sevens, so the answer is 4/52.
There are four cards that are sevens, and 13 that are spades – but one of the spades is also a seven. So the total number of cards that are a seven or a spade is 4 + 13 - 1 = 16. Which means the probability of getting a seven or a spade is 16/52.
Six of the counters are red, and there are 20 in total, so the probability is 6/20.
There are five yellow counters and nine blue, so 14 counters in total that are yellow or blue. Which means the probability of getting a yellow or blue counter is 14/20.
The only colours of counter in the box are red, yellow, or blue, so the only counters that aren't red or blue are yellow. There are five yellows, so the probability of getting a yellow is 5/20.
The chances of a drawing pin landing point-up and point-down aren't equally likely, so using the relative frequency of these events can help you predict the probability of each outcome happening in future. You know the pin has landed point-up 22 out of 100 times, so can guess that the probability of this outcome is 22/100.
You know the probability of a pin landing point-down is 78/100, so if you throw it up 500 times it's likely to land point-down 500 x 78/100 = 390 times.
The probability of getting tails once is 1/2, so the probability of getting tails twice is 1/2 multiplied by 1/2 = 1/4.
With one of the white socks already out of the bag, there are 3 white socks remaining and 4 black ones. So the probability of choosing a white sock is 3/7.
Kelly Oakes is science editor for BuzzFeed and is based in London.
Contact Kelly Oakes at firstname.lastname@example.org.
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