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

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