Answer:
0.375 = 37.5% probability that two of the coins will land ‘heads’ up
Step-by-step explanation:
For each coin, there are only two possible outcomes. Either it lands heads, or it lands tails. The probability of a coin landing heads is independent of any other coin. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Four well-balanced coins.
This means that [tex]n = 4, p = 0.5[/tex]
What are the odds that two of the coins will land ‘heads’ up?
This is P(X = 2).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{4,2}.(0.5)^{2}.(0.5)^{2} = 0.375[/tex]
0.375 = 37.5% probability that two of the coins will land ‘heads’ up
