True or false? in a hotel, 70 percent of the guests pay by american express credit card. suppose the first x-1 guests use non-american express credit cards while the xth guest is the first to use an american express. then p(x=3)=0.083.

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Scarcev2 Scarcev2 · Answer 1 · 2017-11-11T08:48:31+01:00

I would say false but idk dude you have a 50% chance, good luck ^0^

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MrRoyal MrRoyal · Answer 2 · 2021-10-29T19:25:35+02:00

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.