Trisha has 2 boxes of marbles. She selects a marble from each box 100 times, replacing the marble back into its box each time.From the first box, she selects:A white marble 29 timesA red marble 25 timesA blue marble 46 times.From the second box, she selects:A yellow marble 27 times.A green marble 21 timesAn orange marble 52 times.Based on this information, what is the probability that Trisha will select a red marble from the first box and an orange marble from the second box on her next turn?

To find the probability that Trisha will select a red marble from the first box and an orange marble from the second box, we need to calculate the individual probabilities and then multiply them.

1. Probability of selecting a red marble from the first box:
   \[P( \text { Red from first box} ) = \frac { \text { Number of red marbles selected} } { \text { Total selections from first box} } = \frac { 25} { 100} = 0.25\]
2. Probability of selecting an orange marble from the second box:
   \[P( \text { Orange from second box} ) = \frac { \text { Number of orange marbles selected} } { \text { Total selections from second box} } = \frac { 52} { 100} = 0.52\]
3. Probability of both events happening together:
   \[P( \text { Red and Orange} ) = P( \text { Red from first box} ) \times P( \text { Orange from second box} ) = 0.25 \times 0.52 = 0.13\]

Supplemental Knowledge

Probability measures the likelihood that something will take place. When dealing with compound events where multiple events happen together, multiplying each probability separately will give us the probability for both events happening together.

1. Basic Probability:
   • The probability \(P\) of an event occurring is given by:
     \[P( \text { event} ) = \frac { \text { Number of favorable outcomes} } { \text { Total number of outcomes} } \]
2. Compound Probability:
   • For independent events \(A\) and \(B\), the probability that both \(A\) and \(B\) occur is:
     \[P( A \text { and } B) = P( A) \times P( B) \]

Real-World Applications

Probability can help guide decisions in everyday life, from assessing risks to anticipating outcomes and planning strategies. For example, knowing how to calculate the probability of drawing certain cards during card games will aid your strategy planning.
Assume you're organizing a raffle featuring multiple prize categories; knowing the odds for winning each can help determine how many tickets to purchase or which category should receive more focus. 

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