Week 6 Probability and Assessment MATHS Week 6 Probability and Assessment

Multiplication Challenge Multiplication Challenge! You have 5 minutes to fill in as many as you can – good luck!

Answers

Have you done your directed study? Please get your completed worksheet out and be ready to check your answers.

What did we do last week?

What are we going to do this week? Probability Use probability vocabulary, write probabilities as fractions, decimals or percentages and use a probability scale Understand the difference between theoretical and experimental probability Fractions Use and understand proper and improper fractions Convert between proper and improper practions Assessment

Washing Line Activity Yes! ? No! Maybe

Probability

Probability Scale: ¼ ½ ¾ Probability is given as a value between 0 and 1, with 0 being impossible and 1 being certain 0.25 0.75 1 0.5 ¼ ½ ¾ 25% 50% 75% 100%

Probability The probability of an event happening is: The number of ways that event can happen The total number of possible outcomes

What is the chance of getting a 6 with one dice?

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

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 3 6

True or false? 14 questions – true or false?

A 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

B 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.

C 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 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

E 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.

F 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.

G In a group of ten people the probability of two people being born on the same day of the week is 1. True. There are only seven days in a week, so some pair must have been born on the same day.

H 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.

I The probability of getting exactly three heads when I toss a coin six times is ½. False – and there are a large number of possible outcomes. The actual probabilities are shown on the next page.

Number of heads Probability 0.015625 1 0.093750 2 0.234375 3 0.312500 4 5 6 The calculations are based on something called the Binomial Distribution

There is an evens chance of it raining on any given day. J 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.

It is harder to score a double than any other combination of dice. K It is harder to score a double than any other combination of dice. True – see the next slide

Imagine two separate dice, one red and one blue Imagine two separate dice, one red and one blue. The combinations are as follows: Blue Dice 1 2 3 4 5 6 1, 1 1, 2 1, 3 1, 4 1, 5 1, 6 2, 1 2, 2 2, 3 2, 4 2, 5 2, 6 Red 3, 1 3, 2 3, 3 3, 4 3, 5 3, 6 4, 1 4, 2 4, 3 4, 4 4, 5 4, 6 5, 1 5, 2 5, 3 5, 4 5, 5 5, 6 6, 1 6, 2 6, 3 6, 4 6, 5 6, 6 Of the thirty six combinations, only six are doubles, which is not half of all possible results.

False – see the next page. Coming into college I could be early, on time, or late. Therefore the probability of being late is 1/3.

Look at past records. I haven’t been late this year, so the probability is zero. Actually, over a college year, there is a small probability that I just might be late!

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

N 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.

Terminology Probability Likelihood Chance Fraction, Decimal or Percentage Probability Scale

Improper FRactions

Mixed Number – Top Heavy Fraction 1 4 5 Step 1 – multiply the whole number by the denominator. Step 2 – then add the numerator. 9 5 1 x 5 = 5 REMEMBER that the denominator ALWAYS stays the SAME. 5 + 4 = 9 2 1 3 Step 1 – multiply the whole number by the denominator. Step 2 – then add the numerator. 7 3 2 x 3 = 6 REMEMBER that the denominator ALWAYS stays the SAME. 6 + 1 = 7

Mixed Number – Top Heavy Fraction 1. 1 3 10 2. 3 3 4 3. 1 2 7 4. 2 1 4 6. 2 4 5 7. 5 3 8 8. 8 7 9 5. 9 1 2

Top Heavy Fraction – Mixed Number 11 4 Work out how many 4’s go into 11. 2 remainder 3 2 3 4 This gives you: REMEMBER that the denominator ALWAYS stays the SAME.

Top Heavy Fraction – Mixed Number 14 5 13 3 19 2 23 7 1. 2. 3. 4. 14 10 55 6 35 8 12 11 7. 8. 5. 6.

Four operations with mixed number fractions

Directed Study

Learn your times tables! Choose one of the following times table that you struggle with – 6 7 8 LEARN IT!

2nd lesson Half Term Mini Assessment You now have one and a half hours to complete the mini assessment. You are expected to stay for the full time. If you finish the assessment early, use the time wisely to check through your answers.