Probability and Fractions - SAT Math Part 30

TL;DR

Determine the probability of selecting specific marbles and coins, as well as the probability of a student's gender given their chosen course.

Transcript

number 99 a bag contains five red marbles seven yellow marbles eight blue marbles and ten green marbles what is the probability of selecting a red or a green marble well let's begin by organizing the information that we have with all the different colored marbles so we have five red marbles seven yellow marbles eight blue marbles ten green marbles ... Read More

Key Insights

• #️⃣ Probability can be calculated by dividing the number of desired outcomes by the total number of outcomes.
• ❓ Conditional probability involves finding the probability of one event given that another event has already occurred.
• ❓ Simplifying fractions can often make comparisons and calculations easier.
• 💁 Organizing and summarizing information helps in accurately calculating probabilities.
• ✖️ The probability of multiple events occurring is found by multiplying the probabilities of each event individually.
• 👾 The probability of selecting items without replacement changes as the number of items in the sample space decreases with each selection made.
• ⁉️ Understanding the context of the problem is crucial for correctly interpreting and solving probability questions.

Questions & Answers

Q: What is the probability of selecting a red or green marble from the bag?

The probability of selecting a red marble is 5/30, and the probability of selecting a green marble is 10/30. Adding these probabilities together gives a probability of 15/30 or 1/2 for selecting a red or green marble.

Q: What is the probability of selecting a quarter on the first try and then a dime on a second try without replacement?

The probability of selecting a quarter on the first try is 10/25. Considering the second try without replacement, there are 8 dimes out of 24 coins, resulting in a probability of 8/24. Multiplying these probabilities gives a final probability of 2/15.

Q: What is the probability that a randomly chosen student from the school is male?

Out of the 110 tenth-grade students, there are 54 males. Therefore, the probability of selecting a male student is 54/110.

Q: Given that a student is taking geometry, what is the probability that the student is female?

There are 50 students taking geometry, and out of those, 32 are females. Thus, the probability of selecting a female student given that they are taking geometry is 32/50.

Q: What fraction of students taking algebra are male?

Out of the 60 students taking algebra, 36 are males. Therefore, the fraction of students taking algebra who are male is 36/60 or 3/5.

Summary & Key Takeaways

• The first example involves calculating the probability of selecting a red or green marble from a bag containing different colored marbles.

• In the second example, the probability of selecting a quarter and then a dime without replacement from a jar containing nickels, dimes, and quarters is determined.

• The last three examples focus on calculating the probability of a student's gender given a specific course.