Dont understand the answer i was given...?

Question

Please help me to answer....

I have 4 coins i throw them all what is the probability that 3 would be heads. 1/? (one has to be on top.....
The clue is that its a whole number
And could you please show your working out thanks.....

someone answered me like this:
p=(3heads/1 tails)
p=1/2x1/2x1/2x1/2
p=1/16

but how do you get 1/2?

Answer 1

Not sure - why not toss a coin?

Answer 2

Each coin has a 1/2 chance of being a head (H) or Tail (T). We have 4 coins so each situation has a 1/16 chance of happening. Three heads would be
HHHT
HHTH
HTHH
THHH
HHHH
So the chance of getting 3 Heads is 5/16

If 4 heads is not allowed then it is 4/16 = 1/4

The answer is not 1/2. If it was that would mean Heads were more likely than Tails

Answer 3

If you toss a coin, the probability of a head =1/2 ie you have a 50:50 chance of a head.
If you roll a dice the prob. of the number 5, say, is 1/6 ie 1 chance out of 6 possible outcomes.
Prob. of an even no. when rolling a dice = 3/6 ie 3 chances out of 6 possible outcomes.
If there are 3 red balls and 7 blue balls in a bag, prob of picking a blue ball = 7/10
Prob. of red ball = 3/10
In a pack of cards there are 52 cards:-
Prob. of selecting an ace = 4/52 = 1/13
Prob. of selecting a red card = 26/52 = 1/2
Prob. of a queen or king = 8/52 = 2/13
Hope these examples might help.
However, to answer your question, I would consider the number of outcomes possible when 4 coins are tossed This is 16.
The number of outcomes involving 3 heads and 1 tail is 4.
Hence Prob(3 heads) = 4/16 = 1/4

Answer 4

Technically, the answer is 5/16, as '3' in this case means 'at least 3', i.e. 3 or 4.
The Binomial Theorem states that the chance of r successes from n trials with a probability p of success on each trial is

n!
_____ p^r (1-p)^(n-r)
r!(n-r)!

so in this case where p = 1/2 (assuming a fair coin), n=4 and r=3 (defining a head as a success) we get

4!
_____ 0.5^3 * 0.5^1 =
3! 1!

4*3*2*1
=______ 0.5*0.5*0.5*0.5
3*2*1*1


= 4*(1/16) = 1/4

Hope this helps.

Answer 5

The correct answer to the original problem is 1/4.

There are 16 different ways that coins will land. In four of them, there is one tail and three heads.

So the probability of getting exactly three heads (and one tail) is 4 out of 16, or 1/4.

The answer of 1/16 is wrong.

Answer 6

there answer was wrong, but you get 1/2 because each coin has 2 sides so a coin has a 1/2 probability to be Heads or Tails

Answer 7

1/2= 1 out 2 chances of getting a head or tail because there is only two sides to a coin

Answer 8

This is basically the same problem as only having one tail in four coins. If you tossed one coin four times, your chances of only getting one tail would be (1/2)^4 = 1/16.This is because your chance of getting a head is 1/2 and your chance of getting a tail is 1/2 But you tossed four coins, so your chances are four times as great ......1/4.
hhhh =1/16
thhh =1/4
tthh =3/8
ttth =1/4
tttt =1/16
These types of problems are difficult to grasp.

Answer 9

You get 1/2 because each coin has only two sides so you have a one in two chance of the coin landing as heads and a one in two chance of it landing as tails,
I don't think the question expects you to take into account the slim chance of a coin landing on its side.

Answer 10

What we did not understand is the meaning of
"one has to be on top"
But you are right, we did not care about your requirement of a whole number.
¿Could you explain that misterious "one has to be on top"?
¿Do you mean the first coin must be head?

Apart from that, a probability is always 1 or less than 1.
The only possible whole number for a probability is 1.

Answer 11

the answer is 1/4.

possible outcomes that give you 3 Heads and 1 Tail are:

HHHT
HHTH
HTHH
THHH

The total number of possible outcomes is 16 (do you know why?)

so out of these 16 total possible outcomes 4 of them, listed above, satisfy your requirements. So the probability is:

P(3Heads & 1 Tail) = 4/16 =1/4