Presentation on theme: "Nuffield Free-Standing Mathematics Activity"— Presentation transcript:
1 Nuffield Free-Standing Mathematics Activity Probability
2 ProbabilityWhat is the probability of all the coins landing heads up?’What is the probability that the bus does not come on time?Sometimes you can work out probabilities, but sometimes you need to use an experiment or past experience.In this activity you will use both methods.
3 Probability How can you estimate: • the probability that a drawing pin lands point up if you drop it onto the floor?• the probability of a train being late?• the probability of having an accident at home?Experimental probabilityIf drawing pin lands point up in 140 out of 200 throws= 0.7Think about ... In what other situations can data help you to estimate probabilities?The more data you have, the better the estimate.
4 Theoretical probability must be equally likelyIf a fair dice is thrownP(6)Think about ... How do these use the fact that the dice is fair?P(7)= 0P(even)P(less than 7)= 1P(more than 2)Probability lineP(6)P(even)P(more than 2)(impossible)1(certain)P(7)P(less than 7)
5 P(E doesn’t happen)P(E) = 1 – P(E)Think about... What is the probability that the drawing pin lands point down?ExpectationExpected number of trials in which E occurs= P(E) total number of trialsIn 300 throws of a fair diceexpected number of sixes= 50expected number of even scores= 150expected number of scores above 2= 200
6 Possible outcomes – tossing two coins List possibilitiesUse a tableHHHTTHTTHT2nd coin1st coinHH, HT, TH, TTHHTHTTUse a tree diagram2nd coinHTHHProbabilities if coins are fair1st coinHTHTP(two Hs)HTTHP(H&T in any order)TTP(at least one T)
7 Reflect on your workExplain how relative frequency is used to estimate probabilities.Give some examples.Write down a formula for the theoretical probability of an event E.Why is it important to assume that dice and coins are fair when you are calculating theoretical probabilities?Describe three ways of finding probabilities of combined events.