Week 6 Understand and use probability Functional MATHS Week 6 Understand and use probability

This maths trick will “guess” your age To start…. This maths trick will “guess” your age https://www.youtube.com/watch?v=_Up5xtiw1_o

Ratio and Proportion What did we do last week? Solve problems involving ratio : Understand ratio notation Simplify ratios Calculate amounts of parts using ratio Best buys

Simplifying Ratio RECAP…

Writing a ratio and problem solving RECAP…

Solving problems with ratio (Harder) RECAP…

Sharing in a ratio (basic example) RECAP…

Sharing in a ratio (harder example) RECAP…

Sharing in a ratio – your turn

What are we going to do today? Probability Use probability to assess the likelihood of an outcome The language of probability Marking events on the probability scale Calculating probabilities

The likelihood of an outcome Probability The likelihood of an outcome

Probability line activity How can you decide the probability of an event like “I will be struck by lightning this afternoon”? How can you calculate exactly the probability of getting a tail with one toss of a coin?

The probability line activity We will go through some statements and we will need to place these in order from impossible to certain on the line. Where do you think each event will go?

A pregnant lady gives birth to a boy

A lady gives birth to a tiger cub

A pregnant lady gives birth to a boy or a girl

You will be hit by lightning this afternoon

You will get a four with one roll of a dice

You will get a tail with the toss of one coin

You will sleep tonight

You will get a heart when you pick a card from a pack

There will be an earthquake in Lowestoft in the next 3 yrs

The sun will rise in the morning

You will win the lottery in your lifetime

Equal chance

Certain

Impossible

Likely

Unlikely

1

0.5

the number of ways it can happen total number of possible outcomes Vocabulary Even chance Likely More likely Equally likely Very unlikely May happen Impossible Certain Unlikely Possibly 50-50 chance Very likely The probability of something happening is: the number of ways it can happen total number of possible outcomes

The probability Scale

Calculating probabilities

An introduction to simple probability What is the probability of getting a tail in one toss of a coin?

What’s the probability you pick a sweet?

What’s the probability you pick a stick of chewing gum?

What’s the probability you pick a humbug?

Lucy picks a counter at random from a bag. What is the probability of taking a blue counter? What is the probability of taking a purple counter? What is the probability of taking a blue or purple counter?

the number of ways it can happen total number of possible outcomes Remember… The probability of something happening is: the number of ways it can happen total number of possible outcomes Probability can be expressed as a fraction e.g. the probability of throwing ‘heads’ is ½, or as a decimal (1/2 = 0.5 chance)

Calculating Probability examples When you throw a dice, what’s the probability of scoring 6? When you throw a dice, what’s the probability of scoring an odd number?

What is the chance of getting a 6 on this spinner? 2 4 6

What is the chance of getting an odd number on this spinner? 1 2 3 4 5

What are the chances of getting a 6 on this spinner? 5 4 3

What is the chance of picking a blue ball out of the bag?

What is the chance of picking a purple counter out of the bag?

Probabilities add up to 1

Harder exam questions

True or False?

1. When you roll a fair six- sided dice, it is harder to roll a six than a four. False – a fair dice, so all numbers have equal chance

2. Scoring a total of three with two dice is twice as likely as scoring a total of two. True – look at the combinations: next slide

True – look at the combinations: A score of two can only be obtained in one way – a 1 on each dice. A score of three can be obtained in two ways – 1 and 2 or 2 and 1, so the three is twice as likely.

3. In a lottery, the six numbers 3, 12, 26, 37, 44, 45 are more likely to come up than the six numbers 1,2,3,4,5,6. False – each number has the same chance

The probability of two heads is therefore 4. When two coins are tossed there are three possible outcomes: two heads, one head, or no heads. The probability of two heads is therefore False – look at the combinations: next slide

False because there are four outcomes: HH, HT, TH, TT So the probability of HH is one out of four, or

5. In a ‘true or false’ quiz with ten questions, you are certain to get five right if you just guess.  False – you would expect five right, but because of chance it won’t happen every time.

6. After tossing a coin and getting a head five times in a row, the next toss is more likely to be a tail than a head. False – only gamblers believe their luck will change. The probability will be 1/2 each time, whatever happened before.

7. My friend has four daughters. If she has another baby, it is more likely to be a girl than a boy. False, same as with the coin, unless you look at scientific results, which might suggest various things.

There is an evens chance of it raining on any given day. 8. There is an evens chance of it raining on any given day. False – just look at any weather records. It really does not rain on half the days of a year.

The probability of there being an eclipse at noon tomorrow is zero. 9. The probability of there being an eclipse at noon tomorrow is zero. True – again, look at the records.

10. If I play the national lottery, I have just as much chance of winning as anyone else. False – some people may buy lots more tickets than you.

Kahoot: Probability You need to use your mobile phones Go to the following website https://kahoot.it/ When prompted enter the pin (I will give you this) and your name https://play.kahoot.it/#/?quizId=c16f82b6- 881f-41a9-a56d-f7fc65cf48e3

Directed Study

Directed Study Please complete this in your directed study time and bring it to the next session 