Question

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.

Explanation:

Step1: Calculate probability of strawberry from first bag

The first bag has \(8 + 5+7=20\) candies. The probability of selecting a strawberry candy from the first bag, \(P(S_1)\), is \(\frac{7}{20}\) since there are 7 strawberry candies.

Step2: Calculate probability of tamarind from second bag

The second bag has \(11 + 3+6 = 20\) candies. The probability of selecting a tamarind candy from the second bag, \(P(T_2)\), is \(\frac{3}{20}\) since there are 3 tamarind candies.

Step3: Use multiplication rule for independent events

Since the selections from the two bags are independent events, the probability of both events occurring is the product of their individual probabilities. So \(P = P(S_1)\times P(T_2)=\frac{7}{20}\times\frac{3}{20}=\frac{21}{400}\)

Answer:

\(\frac{21}{400}\)