Question

determine whether the two given events are independent. two planets are selected, without replacement, from the list in the table. the events are \the first selected planet is smaller than mars\ and \the second selected planet is larger than uranus.\ the two events are

Explanation:

Step1: Recall the definition of independent events

Two events $A$ and $B$ are independent if $P(A\cap B)=P(A)\times P(B)$. When sampling without - replacement, the outcome of the first selection affects the probability of the second selection.
Let event $A$ be "the first selected planet is smaller than Mars" and event $B$ be "the second selected planet is larger than Uranus".
The probability of event $B$ depends on whether event $A$ has occurred or not. If the first - selected planet is smaller than Mars, then the set of available planets for the second selection is different compared to the case where the first - selected planet is not smaller than Mars.
For example, if the first planet is Mercury (smaller than Mars), then for the second selection, the number of planets and their probabilities of being selected change compared to a situation where the first planet was Jupiter (not smaller than Mars).

Answer:

not independent