Question

let r be the event that elena chooses a red flower from and vase, and w be the event vase.

• $p(r)=\frac{1}{4}$
• $p(w)=\frac{8}{23}$
• $p(r \text{ and } w)=\frac{2}{23}$

move words and a symbol to the blanks to complete the sentence about the events.
the events that elena chooses a red flower and glenn chooses a white flower are $p(r \text{ and } w)$ is ____ to $p(r)$ __ $p(w)$.
(options: independent, equal, +, -)

Explanation:

Step1: Calculate $P(R) \times P(W)$

$P(R) \times P(W) = \frac{1}{4} \times \frac{8}{23} = \frac{8}{92} = \frac{2}{23}$

Step2: Compare to $P(R \text{ and } W)$

We see $P(R \text{ and } W) = \frac{2}{23}$, which matches $P(R) \times P(W)$.

Step3: Define independent events

Two events are independent if $P(A \text{ and } B) = P(A) \times P(B)$.

Answer:

The events that Elena chooses a red flower and Glenn chooses a white flower are independent. $P(R \text{ and } W)$ is equal to $P(R)$ $\boldsymbol{\times}$ $P(W)$.