By using binomial distribution if two coin are tossed 4 times ,find?

What is the chance that you will have two heads?In summary, using the binomial distribution, if two coins are tossed 4 times, the probability of getting 2 heads is 0.4211. Additionally, the probability of getting exactly one head once is 0.4211, and the probability of getting more than 2 tails in 3 times is missing. The expected number of two tails is also missing, as well as the variance of the number of 2 heads.
  • #1
mattamimi
4
0
by using binomial distribution if two coin are tossed 4 times ,find?
1)the probability of 2 heads in 4 times ?
2)the probability of less than one head once?
3)the probability of than 2 tails in 3 times ?
4)the expected number of two tails ?
5)the variance of the number of 2 heads?
 
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  • #2
Welcome to PF!

Hi mattamimi! Welcome to PF! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help …

start with 1). :smile:​
 
  • #3
thank you :)


1.) I think P(x)=4C1*(1/4)^1*(3/4)^3=0.421
 
  • #4
mattamimi said:
1.) I think P(x)=4C1*(1/4)^1*(3/4)^3=0.421

(try using the X2 tag just above the Reply box :wink:)

uhh? that's obviously the probability of one head in 4 times
 
  • #5
sorry,but I couldn't solve it,can you solve the first problem
 
  • #6
Sorry, but you have to do it yourself.

Please can I check that I understand 1) correctly …

is 1) asking for the probability that when 2 coins are tossed 4 times, there will be 2 heads 4 times, ie a total of 8 heads, ie all heads?

And is 2) asking for the probability that there will be 2 tails exactly once (so the other three times are either 2 heads or one of each)?

And what is the missing word in 3)?
 
  • #7
Moderator's note: thread moved from "Set Theory, Logic, Probability, Statistics"
 
  • #8
mattamimi said:
...can you solve the first problem

I think I speak for tiny-tim as well as for myself:
"YES".

Just to clarify, you are flipping two coins and recording the number of heads. Then you repeat this until you have FOUR numbers?
 

Related to By using binomial distribution if two coin are tossed 4 times ,find?

1. What is the binomial distribution?

The binomial distribution is a probability distribution that describes the outcomes of a certain number of independent trials where there are only two possible outcomes. It is used to calculate the probability of obtaining a certain number of successes in a fixed number of trials.

2. How is the binomial distribution used in the context of coin tosses?

In the context of coin tosses, the binomial distribution is used to calculate the probability of obtaining a certain number of heads (or tails) in a fixed number of tosses. This is because there are only two possible outcomes (heads or tails) and each toss is independent of the others.

3. What is the formula for calculating the binomial distribution?

The formula for calculating the binomial distribution is: P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success in each trial.

4. How can the binomial distribution be applied to the scenario of two coins being tossed four times?

In this scenario, the binomial distribution can be used to calculate the probability of obtaining a certain number of heads (or tails) in four coin tosses. For example, if we want to know the probability of getting exactly two heads in four tosses, we can plug in n=4, k=2, and p=0.5 into the formula.

5. What other real-world scenarios can the binomial distribution be applied to?

The binomial distribution can be applied to any situation where there are only two possible outcomes and each trial is independent of the others. This includes scenarios such as flipping a coin, rolling a die, or conducting surveys with yes/no questions. It can also be used in fields such as genetics, finance, and quality control.

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