Probabilities are used to determine the chance of an event.
[tex]\mathbf{P(x =3) = 0.083}[/tex] is false.
The given parameter is:
[tex]\mathbf{p = 70\%}[/tex] ---- probability that a guest pays by American Express.
Given that the first two did not pay by American Express, and the third guest pays.
The probability is calculated using:
[tex]\mathbf{P(x =3) = (1 -p)^2 \times p}[/tex]
So, we have:
[tex]\mathbf{P(x =3) = (1 -70\%)^2 \times 70\%}[/tex]
Express percentage as decimal
[tex]\mathbf{P(x =3) = (1 -0.70)^2 \times 0.70}[/tex]
[tex]\mathbf{P(x =3) = 0.30^2 \times 0.70}[/tex]
[tex]\mathbf{P(x =3) = 0.063}[/tex]
By comparison
[tex]\mathbf{P(x =3) \ne 0.083}[/tex]
Hence, [tex]\mathbf{P(x =3) = 0.083}[/tex] is false.
Read more about probabilities at:
https://brainly.com/question/11234923
