Using the binomial distribution, it is found that there is a 0.03125 = 3.125% probability that all the nickels will land with heads facing up.
For each coin, there are only two possible outcomes, either it lands on heads, or it lands on tails. The landing of a coin is independent of other coins, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
[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:
- 5 nickels, hence [tex]n = 5[/tex].
- They are equally as likely to land on heads or tails, hence [tex]p = 0.5[/tex]
The probability that all the nickels will land with heads facing up is P(X = 5), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 5) = C_{5,5}.(0.5)^{5}.(0.5)^{0} = 0.03125[/tex]
0.03125 = 3.125% probability that all the nickels will land with heads facing up.
A similar problem is given at https://brainly.com/question/24863377
