probability: what are the chances of getting 2 heads???...tricky question-----?

Question

Sergio said " if I toss 2 coins, I can get 2 heads, or 2 tails, or a head and a tail. There fore the probability that i get 2 heads is 1/3.

Sergio is incorrect. Explain why.?


I thouhgh the answer would be 1/3 but it isnt obviously, can anyone tell me the answer, but more importantly explain how they got this? Thanks very much.

Answer 1

When you are computing the probability of a given event such as 2 heads, 2 tails, or one of each, you are essentially counting the number of ways a given event can occur and dividing this number by the number of all possible outcomes.

If you toss 2 coins once ( or one coin twice) there are 4 possible outcomes:

HH = both heads
HT = 1st heads, 2nd tails
TH = 1st tails, 2nd heads
TT = both tails

Assuming the coins are "fair" each outcome is equally likely.

There is one way in four that two heads (or 2 tails) can happen so the probability for each of these outcomes is 1/4
But there are two ways you can have one head and one tail and so the probability of this happening is 2/4 =1/2. The sum of all the probabilities of the distinct outcomes will always equal 1.
1/4 +1/4 + 1/2 =1

How about if you have 3 tosses? The 8 possible outcomes are as follows:

HHH
HHT
HTH
THH
HTT
THT
TTH
TTT
We see there is only one way to have 3 heads (or 3 tails) and so the probability of 3 heads (or 3 tails) = 1/8
However there are 3 ways you can have 2 heads and one tail, so the probability of this happening is 3/8. And there are also 3 ways you can have one head and 2 tails, so 3/8 is the probability for this too.

Answer 2

The probability of getting heads on one toss is 1/2. The probability of getting heads when tossing a second coin is also 1/2. To calculate the probability of heads on one AND on the other, the two independant probabilities are multiplied:
1/2 * 1/2 = 1/4 = 25% Think about it another way: there are four possible outcomes when tossing two coins:

HH
HT
TH
TT

The probability of any one of these 4 outcomes has to be 1 in 4. This is obviously the same result obtained by multiplying the two independent probabilities as shown above

Answer 3

1 in two for each coin so the odds are dpuble to 1/4 because the h/t combination has two for instance coin 1 get heads and coin 2 gets tails then coin 1 can get tails and coin 2 heads, meaning h/t combination has 2/4 (simplified to 1/2) odds and h/h has a 1 in 4 chot as with t/t

Answer 4

If you toss two coins then there are four possiblilties. Remember you have two coins so you can get two heads, two tails or two different combinations of one head one tail (the first coin can be a head and then second a tail or the first coin can be tails and the second heads).
This means there would be 1/4 chance of getting two heads, 1/4 chance of getting two tails and 1/2 chance of getting one of each.

I hope that helped :)

Answer 5

The question is tricking you. Notice that there are two ways to get a head and a tail. Either head first then tail, or tail first then head. Therefore the true set of all possible outcomes is:

HH, HT, TH, TT.

And the probability of getting both heads is then 1/4.

Answer 6

If H= Heads & T= Tails

HH
HT
TH
TT

So therefore, you have a 25% chance of getting 2 heads.

Answer 7

probability is 1/2