Coin toss probability problem

In summary, the question is asking for the probability of getting a head on the first toss given that the total on all three tosses is an odd number. The sample space consists of 8 equally likely outcomes and the probability of getting a head on the first toss can be calculated using the conditional probability formula.
  • #1
naspek
181
0
Hi all =)

Question...
A fair coin is tossed thrice. Supposed we denote a "head" turning up as 1 and
"tail" as 0. Given that the total on all three tosses is an odd number,
what is the probability that at first toss, we get a "head"?

i don't have any idea to start answering this question..
please guide me.. =)
 
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  • #2


Ok our sample space is
[tex]\Omega = \{0,1\}^3 = \{(0,0,0),(0,0,1),(0,1,0),(0,1,1),(1,0,0),(1,0,1),(1,1,0),(1,1,1)\}[/tex]
We assume a fair coin so every outcome is equally likely which gives us the probability function:
[tex]p(x) = \frac{1}{8} \qquad \textrm{for all }x \in \Omega[/tex]
Now we have two events [itex]E_1,E_2[/itex]. Let [itex]E_2[/itex] denote the event that the total on all three tosses is an odd number. Let [itex]E_1[/itex] denote the event that on the first toss we get a head. What you want is the conditional probability [itex]P(E_1|E_2)[/itex]. List all elements in [itex]E_1[/itex] and [itex]E_2[/itex] and you should be able to compute it using the formula:
[tex]P(E_1|E_2) = \frac{P(E_1 \cap E_2)}{P(E_2)}[/tex]
 

1. What is the probability of getting heads or tails when flipping a coin?

The probability of getting heads or tails when flipping a coin is 50%, also known as a 1:1 chance. This means that for any given coin toss, there is an equal chance of getting heads or tails.

2. What is the probability of getting a certain number of heads or tails in a series of coin tosses?

The probability of getting a certain number of heads or tails in a series of coin tosses can be calculated by using the binomial distribution formula. This formula takes into account the number of trials (coin tosses), the probability of success (getting heads or tails), and the desired number of successes. For example, the probability of getting exactly 3 heads in 5 coin tosses is 31.25%.

3. Is it possible to have a coin land on its edge?

Technically, it is possible for a coin to land on its edge, but the probability of this happening is extremely low. This is because coins are designed to have one side slightly heavier than the other, making it more likely for the coin to land on one of its two sides. The probability of a coin landing on its edge is estimated to be around 1 in 6000 tosses.

4. Does the probability of getting heads or tails change over time?

No, the probability of getting heads or tails does not change over time. Each coin toss is an independent event and the outcome of one toss does not affect the outcome of the next. This means that even if a coin has landed on heads 10 times in a row, the probability of getting heads or tails on the 11th toss is still 50%.

5. What is the expected outcome of a series of coin tosses?

The expected outcome of a series of coin tosses is the average number of heads or tails that would be expected based on the probability of success. For example, if you were to toss a coin 10 times, the expected outcome would be 5 heads and 5 tails. However, this does not mean that you will always get this exact outcome, as the actual results may vary due to chance.

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