Question

1. Among 806 people asked which is there favorite seat on a plane, 492 chose the window seat, 8 chose the middle seat, and 306 chose the aisle seat (based on data from USA Today).
One randomly selected person:
a) P (prefers aisle seat) = ___________
Two randomly selected people:
b) P (both prefer aisle seat) with replacement= ___________
c) P (both prefer aisle seat) without replacement = ___________

Answer 1

Answer:

See explanation

Step-by-step explanation:

Among 806 people asked which is there favorite seat on a plane, 492 chose the window seat, 8 chose the middle seat, and 306 chose the aisle seat, then

$P(\text{Window seat})=\dfrac{492}{806}=\dfrac{246}{403}\\ \\P(\text{Middle seat})=\dfrac{8}{806}=\dfrac{4}{403}\\ \\P(\text{Aisle seat})=\dfrac{306}{806}=\dfrac{153}{403}$

a) One randomly selected person preferes aisle seat with probability

$\dfrac{153}{403}$

b) Two randomly selected people both prefer aisle seat (with replacement) is

$\dfrac{306}{806}\cdot \dfrac{306}{806}=\dfrac{153}{403}\cdot \dfrac{153}{403}=\dfrac{23,409}{162,409}$

c) Two randomly selected people both prefer aisle seat (without replacement) is

$\dfrac{306}{806}\cdot \dfrac{305}{805}=\dfrac{153}{403}\cdot \dfrac{61}{161}=\dfrac{9,333}{64,883}$

Answer 2

The probability of a person being selected randomly preferring an aisle seat is 37.96%.

What is Probability?

The probability helps us to know the chances of an event occurring.

$\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}$

We know that 492 chose the window seat, 8 chose the middle seat, and 306 chose the aisle seat based on data from USA Today. therefore, the total number of people that were indulged in the survey are,

$\text{Total Number people in the survey} = 492 + 8 +306 = 806$

A.) We know the formula of the probability, therefore, the desired outcome is the number of people who prefers aisle seat that is 306, while the total possible outcome is the total number of people who participated in the survey.

$\rm{Probability (Aisle\ Seat)=\dfrac{\text{Number of people who prefer aisle seat}}{\text{Total number of people who participated in the survey}}$

$\begin{aligned}\rm{Probability (Aisle\ Seat)&=\dfrac{306}{806}\\\\ &= 0.3796\\\\& = 37.96\%\end{aligned}$

B.) We know the formula of the probability, therefore, the desired outcome is the number of people who prefers aisle seat that is 306, while the total possible outcome is the total number of people who participated in the survey.

But since we need to find out the probability of the two-person being selected and both preferring aisle side, therefore, we need to find the probability twice,

$\begin{aligned}\rm{Probability (Both\ prefer\ Aisle\ Seat)&=\dfrac{306}{806}\times \dfrac{306}{806}\\\\ &= 0.14413\\\\& = 14.413\%\end{aligned}$

C.) We know the formula of the probability, therefore, the desired outcome is the number of people who prefers aisle seat that is 306, while the total possible outcome is the total number of people who participated in the survey.

But since we need to find out the probability of the two-person being selected and both preferring aisle side, also, the passengers can not be replaced.  therefore, we need to find the probability twice but the number of desired outcomes and the total possible outcomes both will be decreasing,

$\begin{aligned}\rm{Probability (Both\ prefer\ Aisle\ Seat)&=\dfrac{306}{806}\times \dfrac{305}{805}\\\\ &= 0.14384\\\\& = 14.384\%\end{aligned}$

Hence, the probability of a person being selected randomly preferring an aisle seat is 37.96%.

Learn more about Probability:

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