Question

A coin is tossed 20 times. it lands heads 4 times. Compare the experimental probability to its theoretical probability. If the probabilities are not close, explain a possible reason for the discrepancy.

Can anyone help me please? I need help for a test tomorrow!
@jim_thompson5910 @dan815 @mathstudent55 @e.mccormick @perl @TheSmartOne @jhonyy9 @pooja195 @Compassionate @M4thM1nd

Answer 1

Hello m4th M1nd :D

Answer 2

Hello^^

Answer 3

The chances to get head in one flip is \(1/2\)

Answer 4

yes

Answer 5

Sorry but i'm not sure how to solve this one :(

Answer 6

you arent? :(

Answer 7

are you good at probability :(?

Answer 8

@TheSmartOne can you help?

Answer 9

@mathmate ?

Answer 10

@dan815

Answer 11

We all realize that the theoretical probability is 10 heads out of 20, do you agree?

Answer 12

why

Answer 13

I understand the possibility of both sides can be 50%

Answer 14

Because the probability of having heads is 1/2 for \(each\) toss (assuming a fair coin).

Answer 15

correct

Answer 16

With two tosses, we expect 1 heads, and with 20 tosses, we expect 10 heads, agree?

Answer 17

Correct

Answer 18

The key to the question is to find the probability of tossing 4 heads, and decide if it is a likely outcome.

Answer 19

oh

Answer 20

so it is not.

Answer 21

For example, if we get 9 heads instead of 10, we won't even blink.

Answer 22

so it is not a likley outcome.

Answer 23

If we get eight, we say, it's not impossible. For seven, we say, hmmm....
Where do we draw the line? That's when probability comes in.

Answer 24

To justify that getting 4 heads out of 20, we need to calculate the probability of this outcome... using binomial distribution.
Have you covered binomial in class?

Answer 25

so 4/20 is not a likley outcome because 20 % is not near 50%

Answer 26

The probability is not proportional to the number of heads.
getting 1 heads out of 20 is VERY much unlikely, less than 10 time getting 10 heads.
That's why we need binomial distribution.

Answer 27

so what do we do?

Answer 28

*

Answer 29

calculate the probability of getting 4 heads out of 20, and see if the probability is less than 5%, or happening once in 20 times, which is the normal cut off for "unlikely" events.

Answer 30

so how would I do that .. haha..

Answer 31

The binomial probability for n trials each with probability p, and with an outcome of r successes is given by
P(r)=C(n,r)p^r*(1-p)^(n-r)
where C (n,r)=n!/(r!(n-r)!)

Answer 32

o_o?

Answer 33

Can you substitute the numerical values for n, r, and p?

Answer 34

Is this 7th grade math?

Answer 35

Oh, ....

Answer 36

In that case, you do not do the quantitative part.
You will say that the probability of getting 4 heads out of 20 is very small, then what else can you say?

Answer 37

...or what do you suspect?

Answer 38

Im really confused.

Answer 39

What do you think could be a reason for such "freak" occurrence (with probability 0.005)?

Answer 40

mathmate, if you flip a coin 1000 times, and you calculate the probability of getting exactly 500 heads , using a binomial distribution its a very small probability

Answer 41

Math mate I don't know what your talking about...

Answer 42

@perl true, I guess P(<=4) would be a just measure!

Answer 43

mathmate, ok you mean if the probability of getting 4 heads or less out of 20 , then there is evidence it could be a loaded coin

Answer 44

Remember earlier I said "assuming a fair coin"?
In that case, the outcome would be around ten out of 20, right?

Answer 45

A coin is tossed 20 times. it lands heads 4 times. Compare the experimental probability to its theoretical probability. If the probabilities are not close, explain a possible reason for the discrepancy.

(Question restated)

Answer 46

yes math mate

Answer 47

andrew, there are two possibilities. either the coin landed on heads 4 times by chance, or the coin is loaded.

Answer 48

@perl I mean what could be a better indication is if P(<=4) is small, then there is a good indication of some anomaly.

Answer 49

Ok.

Answer 50

So what do I do in this problem?

Answer 51

@Andrewthehelper
If the coin is not a fair coin (we call it a loaded coin) by chance or by intention, it will not have a 50-50 probability of landing on heads. right?

Answer 52

Yes

Answer 53

So would that be a possible explanation of the discrepancy?
An other possibility is that we could hit an unlikely outcome even if the coin is fair.

Answer 54

OHH

Answer 55

Can you define probability in your own words for me?

Answer 56

It's a similar situation to a family having 7 girls and no boys. It is unlikely, but not impossible.

Answer 57

and I have another question

Answer 58

In very rough terms, probability is a number between the two limits 0 (impossible) and 1 (certainty) that describes the likelyhood of an event occurring.

Answer 59

ok heres the next question

Answer 60

The proper definition of probability requires more concepts.

Answer 61

Im gonna say my answer and your going to see if its correct

Answer 62

Yes, I like that.

Answer 63

A weather forcaster predicts a 30 % chance of rain for each of the next three days. Describe a way to simulate the chance it will rain the next three days

Answer 64

Thats my question

Answer 65

heres my answer

Answer 66

you can put 3 black marbles and 7 blue marbles in a bag and pick every day to see what it will be each day

Answer 67

Correct?

Answer 68

yes, that would be a good experiment.
You only have to add that after each marble is picked, you will replace it in the bag before the next draw. This is called "with replacement".

Answer 69

Correct :)

Answer 70

"with replacement", we ensure that the probability of picking the black marble remains at 30%.

Answer 71

Can you also do this?

Answer 72

Put 3 black on a spinner and 7 blue on a spinner equally. and spin to see what it is?

Answer 73

Each day.

Answer 74

Yes, that would be fine. I would also specify that there are 10 equal sectors on the spinner.

Answer 75

:) ok

Answer 76

Im really confused on experimental and theorticial probability though.

Answer 77

Can you help me perl?

Answer 78

theoretical probability is the probability you know just by thinking about the situation, theoretically

Answer 79

you know theoretically there is a 50% chance that a coin lands on heads, even before you actually flip it

Answer 80

isnt theoretical probability like favorable outcomes/total?

Answer 81

Yes perl

Answer 82

Experimental probability can have different results when you repeat the experiment many times. Theoretical should have only one "calculated" result.

Answer 83

so can I give an example?

Answer 84

ok I got one

Answer 85

A number cube is rolled 20 times and lands 1 two times and on 5 four times. Find each experimental probability. Then compare the experimental probability to the theoritical probability

A. probability of it landing on 5 is?

B. probability of it not landing on 1 is?

Answer 86

anyone?

Answer 87

$$\Large probability = \frac{no. favorable}{ no. total} $$

Answer 88

ok so.

Answer 89

5 is the number of favorable and 20 is the total so it is 1/20

Answer 90

Correct?

Answer 91

Of it not landing on 1 is 19/20

Answer 92

am I wrong?

Answer 93

it says it lands on 5 four times, so it should be 4 / 20 for experimental probability

Answer 94

that is the probability you found by doing the experiment (actually rolling the die twenty times)

Answer 95

oh

Answer 96

So how about not landing on 1?