Alright, let's solve this step by step:
1. Determine the total number of marbles in the bay:
- Blue marbles: [tex]\( 4 \)[/tex]
- Red marbles: [tex]\( 3 \)[/tex]
- White marbles: [tex]\( 2 \)[/tex]
To find the total number of marbles, we simply add them all together:
[tex]\[
\text{Total marbles} = 4 (\text{blue}) + 3 (\text{red}) + 2 (\text{white}) = 9
\][/tex]
So, the total number of marbles is [tex]\( 9 \)[/tex].
2. Calculate the probability of picking a red marble at random:
- The number of red marbles is [tex]\( 3 \)[/tex].
- The total number of marbles is [tex]\( 9 \)[/tex].
The probability [tex]\( P \)[/tex] of an event is given by the formula:
[tex]\[
P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\][/tex]
Applying this formula to our problem, the probability of picking a red marble:
[tex]\[
P(\text{red marble}) = \frac{3 (\text{red marbles})}{9 (\text{total marbles})} = \frac{3}{9} = \frac{1}{3}
\][/tex]
This simplifies to approximately [tex]\( 0.3333 \)[/tex] (or [tex]\( \frac{1}{3} \)[/tex] in exact fractional form).
Thus, summarizing our results:
- The total number of marbles in the bay is [tex]\( 9 \)[/tex].
- The probability of picking a red marble at random is [tex]\( 0.3333 \)[/tex] (or [tex]\( \frac{1}{3} \)[/tex]).
This is the detailed solution to the problem given.
