Perform an experiment to show that as the number of trials increases, the relative frequency approaches the probability of a coin toss. Perform 10, 20, 50, 100, 200 trials of tossing a coin.
Probability identities
The following results apply to probabilities, for the sample space
$S$ and two events
$A$ and
$B$ , within
$S$ .
Notice how we have used
$P(C\cup A)=P\left(C\right)+P\left(A\right)-P(C\cap A)$ .
The following video provides a brief summary of some of the work covered so far.
Probability identities
Answer the following questions
Rory is target shooting. His probability of hitting the target is
$\mathrm{0,7}$ . He fires five shots. What is the probability that all five shots miss the center?
An archer is shooting arrows at a bullseye. The probability that an arrow hits the bullseye is
$\mathrm{0,4}$ . If she fires three arrows, what is the probability that all the arrows hit the bullseye?
A dice with the numbers 1,3,5,7,9,11 on it is rolled. Also a fair coin is tossed. What is the probability that:
A tail is tossed and a 9 rolled?
A head is tossed and a 3 rolled?
Four children take a test. The probability of each one passing is as follows. Sarah:
$\mathrm{0,8}$ , Kosma:
$\mathrm{0,5}$ , Heather:
$\mathrm{0,6}$ , Wendy:
$\mathrm{0,9}$ . What is the probability that:
all four pass?
all four fail?
With a single pick from a pack of 52 cards what is the probability that the card will be an ace or a black card?
Mutually exclusive events
Mutually exclusive events are events, which cannot be true at the same time.
Examples of mutually exclusive events are:
A die landing on an even number or landing on an odd number.
A student passing or failing an exam
A tossed coin landing on heads or landing on tails
This means that if we examine the elements of the sets that make up
$A$ and
$B$ there will be no elements in common. Therefore,
$A\cap B=\varnothing $ (where
$\varnothing $ refers to the empty set). Since,
$P(A\cap B)=0$ , equation
[link] becomes:
$$P(A\cup B)=P\left(A\right)+P\left(B\right)$$
for mutually exclusive events.
Mutually exclusive events
Answer the following questions
A box contains coloured blocks. The number of each colour is given in the following table.
Colour
Purple
Orange
White
Pink
Number of blocks
24
32
41
19
A block is selected randomly. What is the probability that the block will be:
purple
purple or white
pink and orange
not orange?
A small private school has a class with children of various ages. The table gies the number of pupils of each age in the class.
3 years female
3 years male
4 years female
4 years male
5 years female
5 years male
6
2
5
7
4
6
If a pupil is selceted at random what is the probability that the pupil will be:
a female
a 4 year old male
aged 3 or 4
aged 3 and 4
not 5
either 3 or female?
Fiona has 85 labeled discs, which are numbered from 1 to 85. If a disc is selected at random what is the probability that the disc number:
ends with 5
can be multiplied by 3
can be multiplied by 6
is number 65
is not a multiple of 5
is a multiple of 4 or 3
is a multiple of 2 and 6
is number 1?
Questions & Answers
Is there any normative that regulates the use of silver nanoparticles?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?