Question

A fair coin is tossed four times. Find the probability of obtaining: two heads and two tails

Answer 1

ummm well first find how many different ways you can get two heads and two tails tossing 4 times... can you do that?

Answer 2

yes i came up with 6 (HHTT, HTTH, TTHH, HTHT, THTH, THHT)

Answer 3

good... and how many total outcomes are there?

Answer 4

16

Answer 5

6/16

Answer 6

good again... and just divide the two and you got it... but instead of writing down the sample space and finding all the ones with two H's and two T's, do you know how to put it in the calculator?

Answer 7

but what if the coin was tossed a 100 times then how can we find the answer?

Answer 8

thats where you would need the calculator for sure... so if it was tossed 100 times, how many times do they want H and T

Answer 9

say 30 heads and 70 tails

Answer 10

okay no problem... so in the calculator you are going to need to find the nCr, which stands for Combinations.... you could use that by tying
100nCr30 into the calculator
or just use the formula which is
(100!)/30!*70!

Answer 11

if you have a TI 85 or above, its probably got to push MATH first then scroll to PRB and then scroll down.

Answer 12

so the best way to do it is by using a calculator

Answer 13

I would, for example the problem you had...if you type
4nCr2, which mean 4 combo 2, it will give you 6.

Answer 14

keep in mind though, this is only good for when order is not important

Answer 15

there is this last question that is bothering me. i know p=3/5, n=5 but i dont know what k is equal to

Answer 16

what is the entire question

Answer 17

the question is: a weighted coin is biased such that a tail comes up 60% of the time. the coin tossed 5 times. find the probabability of obtaining: tails on the first four tosses only

Answer 18

okay, so what is the probability that there is a tails if we were to only toss it once?

Answer 19

actually more specific, the FIRST toss

Answer 20

sorry i couldnt get back to you because something was wrong with the website

Answer 21

no biggie. did you figure it out.

Answer 22

no i couldnt but answering your question it should be 1/2 for each toss

Answer 23

but the problem is that it is biased 60/100=3/5

Answer 24

are the the four tosses treated as independently?

Answer 25

so the first toss probability of tails is (3/5) second (3/5) third (3/5) fourth (3/5) but finall on the last toss you want heads so that is 2/5. so to find probability you just take 3/5 four times multiplied by 2/5
p=(3/5)^4(2/5)

Answer 26

so should be around .05

Answer 27

the answer is correct :)

Answer 28

so when coins are biased we cant use the formula to find the answer?

Answer 29

what formula do they give you?

Answer 30

bernolli

Answer 31

you could use that formula if order wasnt important... but the fact that they tell you that you must get a tails the first four times no longer makes this problem a combination problem... if it would of said you toss it 5 times and all they want is just 4 tails, then you could, b/c that will let you get a heads on any of the 5 tosses as long as it happens only once... your problem says the heads must occur on the final toss

Answer 32

thanks a lot. i really appreciate your help :) and i really like how you explained it to me

Answer 33

yw

Answer 34

could you just have a look if i am answering this question right?

Answer 35

sure.

Answer 36

55% of the local municipality support the local council. If 8 people are selected at random, find the probability that: half support the council

Answer 37

k=8, p=55/100=11/20

Answer 38

am i right here?

Answer 39

no, give me a few. should be more than that i would think.

Answer 40

mmm i am clueless :)

Answer 41

do they want exactly 4 or atleast 4?

Answer 42

if 8 people are selected randomly

Answer 43

right, 8 people are chosen, but to me it is asking the probability of 4 supporting the council.... OR , atleast 4 support the council

Answer 44

would it be n=8 and k=4

Answer 45

no it is asking for the probability of 4 supporting the council

Answer 46

if the problem is asking for 4 exactly out of the 8, then use the bernoulli formula.

8nCr4*.55^4*.45^4

Answer 47

ill have a look if it is the right answer. it looks right to me

Answer 48

it should be .263 or so

Answer 49

your right as always :)

Answer 50

did you understand how we did that?

Answer 51

yes i got it so n=8 and k=4

Answer 52

if you have one that says atleast 4, then that would be a total different calculation... but let me know if you got any more.

Answer 53

thanks :)

Answer 54

yw

Answer 55

The probability of Colin beating Maria at golf is 0.4. If they play once a week throughout the entire year and the outcome of each game is independent of any other, find the probability that they will have won the same number of matches

Answer 56

I guess p=0.4 and q=0.6

Answer 57

Would n be equal to the number of games they played?

Answer 58

And k will be equal to half of n?

Answer 59

yeah same formula
(52nCr26)(.4^26)(.6^26) = approx. .038

Answer 60

How can we calculate the factorial. Is there a factorial calculator that can give me the answer

Answer 61

TI calculators will do it... anyone that is above a TI-83 i believe.

Answer 62

A new drug being trialled gives 8% of the patients a violent reaction. If 200 patients trial the drug, find the probability that 12 patients have a violent reaction to the drug

Answer 63

P=0.08

Answer 64

Will n be 20?

Answer 65

Sorry 200

Answer 66

And k =12

Answer 67

@zonazoo