Probability of 4-Quarter Flips: Outcomes & Expected Value/Std Dev

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In summary, the conversation is discussing an experiment of flipping four quarters at a time, which has 16 possible outcomes. The random variable X represents the number of heads obtained in a flip, and the probability of obtaining 0, 1, 2, 3, or 4 heads is being calculated. The conversation also mentions representing the probability distribution of X in a table form, and finding the expected value and standard deviation of X.
  • #1
lightningzcobra
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(a).Four quarters were flipped at a time and we know there are 16 possible outcomes.
(i).List all the possible outcomes of the sample space of the experiment above.
(3
(b). X is defined as the random variable of getting heads on a flip of these four quarters. Find the probability of getting
(i). Exactly no heads.
(ii).Exactly one head.
(iii).Exactly two heads.
(iv).Exactly three heads.
(v).Exactly four heads.
(c). (i).Represent the probability distribution of X in (b) above in a table form and use your table to answer the following.
(ii).Find the expected value of X.
(III). Find the standard deviation of X.

Pleasee need help this jst one problem messing me up
 
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  • #2
Hello and welcome to MHB, lightningzcobra! :D

Interesting username...any relation to products from SVT? (Wink)

Can you show us what you have tried so far so our helpers have a better idea where you are stuck and what you may be doing wrong?
 

FAQ: Probability of 4-Quarter Flips: Outcomes & Expected Value/Std Dev

1. What is the probability of getting exactly 4 heads in 4 coin flips?

The probability of getting exactly 4 heads in 4 coin flips is 1/16 or 0.0625. This can be calculated by taking the total number of possible outcomes (2^4 = 16) and dividing it by the number of outcomes that result in exactly 4 heads (1).

2. How many possible outcomes are there in 4 coin flips?

There are 16 possible outcomes in 4 coin flips. This can be calculated by taking 2 (the number of outcomes for each coin flip) and raising it to the power of 4 (the number of flips).

3. What is the expected value of getting 4 heads in 4 coin flips?

The expected value of getting 4 heads in 4 coin flips is 1. This is because there is only one outcome that results in exactly 4 heads, so the probability of this outcome occurring is 1/16.

4. What is the standard deviation of getting 4 heads in 4 coin flips?

The standard deviation of getting 4 heads in 4 coin flips is 0. This is because there is no variation in the number of heads that can occur in 4 coin flips, as there is only one possible outcome that results in exactly 4 heads.

5. How can I increase the probability of getting 4 heads in 4 coin flips?

The only way to increase the probability of getting 4 heads in 4 coin flips is to increase the number of coin flips. The more flips that are performed, the higher the chances of getting exactly 4 heads in a row.

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