SAT Question f496d2c0: Probability And Conditional Probability answer and explanation with Desmos solution

Choice B is correct. It’s given that the proportion of rooms with less than $18$ seats is $26\%$, which is equivalent to $0.26$. It’s also given that the proportion of rooms with $18$ – $40$ seats is $21\%$, or $0.21$; that the proportion of rooms with $41$ – $65$ seats is $29\%$, or $0.29$; and that the proportion of rooms with greater than $65$ seats is $24\%$, or $0.24$. The probability of selecting a room that has a seating capacity greater than $65$ seats given that the room has a seating capacity of at least $18$ seats is equal to the proportion of rooms that have a seating capacity of greater than $65$ seats divided by the proportion of rooms that have a seating capacity of at least $18$ seats. Rooms with a seating capacity of at least $18$ seats include the categories $18$ – $40$ seats, $41$ – $65$ seats, and greater than $65$ seats, so the total proportion for this condition can be written as $0.21+0.29+0.24$, or $0.74$. Therefore, the probability of selecting a room that has a seating capacity greater than $65$ seats given that it has a seating capacity of at least $18$ seats is $\frac{0.24}{0.74}$, or approximately $0.324$. Of the given choices, $0.32$ is closest to $0.324$.