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A student has a penny, nickel, dime, and a quarter. She flips them all simultaneously and checks for heads or tails. What is the probability that all four coins will come up heads

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Answer:

1/ 16

Step-by-step explanation:

Flipping a coin = HT ( 2 possibilities)

Hence, total possibility (n) of flipping 4 coins

n = 2^4 = 2 * 2 * 2 * 2 = 16 possible outcomes

(HHHH, THHH, HHHT, THHT, HHTH, THTH, HHTT, THTT, HTHH, TTHH, HTHT, TTHT, HTTH TTTH, HTTT, TTTT

Probability (A) = required outcomes of A / total possible outcomes

Hence, probability that all coins comes up head :

Number of required outcome = 1

Total possible outcomes = 16

Hence,

P(all heads) = 1/16

Using the binomial distribution, it is found that there is a 0.0625 = 6.25% probability that all four coins will come up heads.

For each coin, there are only two possible outcomes, either it is heads, or tails. The outcome of each coin is independent of other coins, hence, the binomial distribution is used to solve this question.

What is the binomial probability distribution formula?

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

  • x is the number of successes.
  • n is the number of trials.
  • p is the probability of a success on a single trial.

In this problem:

  • A coin is equally as likely to come heads or tails, hence [tex]p = 0.5[/tex].
  • The student has 4 coins, hence [tex]n = 4[/tex].

The probability that all four coins will come up heads is P(X = 4), hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 4) = C_{4,4}.(0.5)^{4}.(0.5)^{0} = 0.0625[/tex]

0.0625 = 6.25% probability that all four coins will come up heads.

You can learn more about the binomial distribution at https://brainly.com/question/24863377

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