Julio has two bags of gummy candies. One at a time, he randomly pulled 8 pineapple, 5 lime, and 7 strawberry candies out of the first bag and put them back each time. He also randomly pulled 11 mango, 3 tamarind, and 6 watermelon candies out of the second bag and put them back each time.Based on this information, what is the probability that Julio will select a strawberry candy from the first bag and a tamarind candy from the second bag the next time he takes a candy from each bag?Type a number in each box. □ /□

1. Determine the probability of selecting a strawberry candy from the first bag:
   • Total candies in the first bag: \(8 + 5 + 7 = 20\)
   • Probability of selecting a strawberry candy: \(\frac { 7} { 20} \)
2. Determine the probability of selecting a tamarind candy from the second bag:
   • Total candies in the second bag: \(11 + 3 + 6 = 20\)
   • Probability of selecting a tamarind candy: \(\frac { 3} { 20} \)
3. Multiply the probabilities of the two independent events:
   • Probability of selecting a strawberry candy and then a tamarind candy: 
     \(\frac { 7} { 20} \times \frac { 3} { 20} = \frac { 21} { 400} \)

Supplemental Knowledge

Probability, particularly when applied to compound events (multiple events occurring simultaneously), requires you to calculate each event individually before adding their probabilities together. A key principle here is multiplication rule for independent events: If two events are independent then their combined probabilities equal that product of individual probabilities.
For example, if you have two independent events:

• Event A: Rolling a 4 on a fair six-sided die.
• Event B: Flipping heads on a fair coin.
  The probability of rolling a 4 (Event A) is 1/6, and the probability of flipping heads (Event B) is 1/2. To find the probability of both events happening together (rolling a 4 and flipping heads), you multiply their probabilities:
  (1/6) * (1/2) = 1/12

Everyday Examples

Imagine yourself at a carnival playing games; one involves selecting colored balls from a bag while the other involves spinning a wheel with various sections. If your aim is to win prizes from both simultaneously, knowing compound probabilities helps assess your odds; for instance if there's only a 1 in 10 chance of drawing red balls and 1/5 of landing on blue in your wheel spin then knowing your combined chance as 1/10 * 1/5 = 1/50 will provide realistic expectations of what could occur in both activities simultaneously.

Probability concepts are not just theoretical; they have practical applications in everyday decision-making and risk assessment. At UpStudy, we provide tools and resources to help you master these essential skills. Our live tutor question bank and AI-powered problem-solving services offer personalized support for all your learning needs. 
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