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# Probability

S2 Probability Lessons

by

Tweet## Pamela Hart

on 27 May 2013#### Transcript of Probability

Prefers Football Prefers Hockey Girls Boys Probability Probability is the measure of chance... In words.... On a scale.... 'likely' 'certain' 'impossible' 'fifty-fifty' impossible Unlikely fifty-fifty likely certain a t-rex flying through the window Mrs Hart winning the lottery winning a coin toss it will rain this week you will get homework today :-) but, in maths we like numbers... more precisely... impossible Unlikely fifty-fifty likely certain 0 0.5 1 P= number of favourable outcomes number of possible outcomes e.g. in a coin toss P(heads)= 1 2 The Basics Examples Assumed Knowledge From S1:

Prime numbers, factors,

multiples,

square numbers etc. From a deck of cards.... 1. What is the probability

of picking a red card? P(red)= 1 2 2. What is the probability

of picking a spade? P(spade)= 1 4 3. What is the probability

of picking a heart less

than 9? P(H,<9)= 2 13 In a bag there are 12 white marbles, 6 green marbles and 9 red marbles. 1. What is the probability

of picking a white marble? P(white)= 12 27 2. The white marble is removed from the

bag.What is the probability of picking a

green or red marble? P(red or green)= 15 26 3. What is the probability

of picking a blue marble? P(spade)= 1 13 P(blue)=0 Two-way tables 16 44 46 14 120 pupils in S2 were asked whether they preferred playing football or hockey. The results are displayed below. Find the probability that a person chosen at random from this group is

(a) a girl

(b) a boy who prefers football

(c) a person who prefers hockey (c) P(hockey)=60/120=1/2 (a) P(girl)=62/120=31/60 (b) P(boy, football)=44/120=11/30 Remember If something is certain to occur

then it has a probability of 1. P= number of favourable outcomes number of possible outcomes P= number of favourable outcomes number of possible outcomes If something is impossible,

the probability of it happening is zero! Now Complete:

Pg 177-178, Ex 14.1

&

Pg 181-182, Ex 14.3

(even questions) Now complete Pg 179,

Ex 14.2 Predictions Monty Hall Think it through... Goat Goat Car Goat Goat Car Goat Goat Car There are 3 options: Option 1:

You pick door 1 (a goat)

The host opens door 2 (a goat)

If you change you win! Option 3:

You pick door 3 (the car)

The host opens door 1 (a goat)

If you change you lose! Therefore, if you play the game you should change if given the option. That way, you have a 2 in 3 chance of winning as opposed to a 2 in 3 chance of getting a goat!! Option 2:

You pick door 2 (a goat)

The host opens door 1 (a goat)

If you change you win! Note:

We are looking at theoretical probability,

what do you think 'experimental probability' is? Independent events Two spinners, like the one shown below, are spun at the same time.

What is the probability that:

(a) the total score is 5?

(b) the total of the

scores is odd? How can I find all the possibilities? Draw a table! 1 2 3 4 5 6 7 8 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 2 4 6 8 3 4 5 5 3 4 5 5 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 9 9 9 9 9 9 9 9 10 11 12 13 14 15 16 15 14 14 13 13 13 12 12 12 12 11 11 11 11 11 10 10 10 10 10 10 (a) P(5)=4/64=1/16 (b) P(odd)=32/64=1/2 Probability can be used to make predictions. Can you think of an example? Examples 1. Seven out of ten people in

Edinburgh voted in the last

general election. Out of

the 150 staff in GHS, how many

would you expect to have voted?

2. If a die is rolled 180 times how

many fives can be expected? 1. 105 2. 30 Extension Questions 1. Which of these numbers cannot be a probability?

a) -0.00001

b) 0.5

c) 1.001

d) 0

e) 1

f) 20%

2. If you toss a coin 3 times in a row, what is the

probability of getting 3 heads?

3. Lawrence parked his car in a parking lot at a

randomly chosen time between 2:30 PM and

4:00 PM. Exactly half an hour later he drove his

car out of the parking lot. What is the probability

that he left the parking lot after 4:00 PM? Page 182-183

Ex 14.4 Now complete: a) and c) P(3 heads)=1/8 P(after 4pm)=1/20

Full transcriptPrime numbers, factors,

multiples,

square numbers etc. From a deck of cards.... 1. What is the probability

of picking a red card? P(red)= 1 2 2. What is the probability

of picking a spade? P(spade)= 1 4 3. What is the probability

of picking a heart less

than 9? P(H,<9)= 2 13 In a bag there are 12 white marbles, 6 green marbles and 9 red marbles. 1. What is the probability

of picking a white marble? P(white)= 12 27 2. The white marble is removed from the

bag.What is the probability of picking a

green or red marble? P(red or green)= 15 26 3. What is the probability

of picking a blue marble? P(spade)= 1 13 P(blue)=0 Two-way tables 16 44 46 14 120 pupils in S2 were asked whether they preferred playing football or hockey. The results are displayed below. Find the probability that a person chosen at random from this group is

(a) a girl

(b) a boy who prefers football

(c) a person who prefers hockey (c) P(hockey)=60/120=1/2 (a) P(girl)=62/120=31/60 (b) P(boy, football)=44/120=11/30 Remember If something is certain to occur

then it has a probability of 1. P= number of favourable outcomes number of possible outcomes P= number of favourable outcomes number of possible outcomes If something is impossible,

the probability of it happening is zero! Now Complete:

Pg 177-178, Ex 14.1

&

Pg 181-182, Ex 14.3

(even questions) Now complete Pg 179,

Ex 14.2 Predictions Monty Hall Think it through... Goat Goat Car Goat Goat Car Goat Goat Car There are 3 options: Option 1:

You pick door 1 (a goat)

The host opens door 2 (a goat)

If you change you win! Option 3:

You pick door 3 (the car)

The host opens door 1 (a goat)

If you change you lose! Therefore, if you play the game you should change if given the option. That way, you have a 2 in 3 chance of winning as opposed to a 2 in 3 chance of getting a goat!! Option 2:

You pick door 2 (a goat)

The host opens door 1 (a goat)

If you change you win! Note:

We are looking at theoretical probability,

what do you think 'experimental probability' is? Independent events Two spinners, like the one shown below, are spun at the same time.

What is the probability that:

(a) the total score is 5?

(b) the total of the

scores is odd? How can I find all the possibilities? Draw a table! 1 2 3 4 5 6 7 8 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 2 4 6 8 3 4 5 5 3 4 5 5 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 9 9 9 9 9 9 9 9 10 11 12 13 14 15 16 15 14 14 13 13 13 12 12 12 12 11 11 11 11 11 10 10 10 10 10 10 (a) P(5)=4/64=1/16 (b) P(odd)=32/64=1/2 Probability can be used to make predictions. Can you think of an example? Examples 1. Seven out of ten people in

Edinburgh voted in the last

general election. Out of

the 150 staff in GHS, how many

would you expect to have voted?

2. If a die is rolled 180 times how

many fives can be expected? 1. 105 2. 30 Extension Questions 1. Which of these numbers cannot be a probability?

a) -0.00001

b) 0.5

c) 1.001

d) 0

e) 1

f) 20%

2. If you toss a coin 3 times in a row, what is the

probability of getting 3 heads?

3. Lawrence parked his car in a parking lot at a

randomly chosen time between 2:30 PM and

4:00 PM. Exactly half an hour later he drove his

car out of the parking lot. What is the probability

that he left the parking lot after 4:00 PM? Page 182-183

Ex 14.4 Now complete: a) and c) P(3 heads)=1/8 P(after 4pm)=1/20