Question

suppose you have a bag with 20 letter tiles in it and 3 of the tiles are the letter b. if you pick a letter tile at random from the bag, the probability that it is the letter b... suppose another bag has 300 letter tiles in it and 216 of the tiles are the letter b. write the probability of picking a tile that is the letter b as a fraction and as a decimal. from which bag are you more likely to pick a tile that is the letter b?
as a fraction is \square.
simplify your answer.)

Explanation:

Step1: Recall Probability Formula

The probability \( P \) of an event is given by the number of favorable outcomes divided by the total number of possible outcomes. So, \( P = \frac{\text{Number of B tiles}}{\text{Total number of tiles}} \).

Step2: Identify Values for Second Bag

For the second bag, the number of B tiles is 216, and the total number of tiles is 300. So we substitute these values into the formula: \( P = \frac{216}{300} \).

Step3: Simplify the Fraction

To simplify \( \frac{216}{300} \), we find the greatest common divisor (GCD) of 216 and 300. The GCD of 216 and 300 is 12. Divide both the numerator and the denominator by 12: \( \frac{216 \div 12}{300 \div 12} = \frac{18}{25} \). Wait, no, wait: 216 ÷ 12 = 18? Wait, 12×18 = 216? 12×18 = 216, yes. 300 ÷ 12 = 25. Wait, but let's check again. Wait, 216 and 300: let's divide numerator and denominator by 12: 216/12 = 18, 300/12 = 25. Wait, but 18 and 25 have no common divisors (GCD of 18 and 25 is 1), so that's simplified. Wait, but wait, maybe I made a mistake. Wait, 216 and 300: let's check GCD. Prime factors of 216: 2³×3³. Prime factors of 300: 2²×3×5². So common factors are 2²×3 = 12. So yes, dividing by 12 gives 18/25. Wait, but wait, the first bag: 3/20. Let's compare 3/20 and 18/25. To compare, find a common denominator. 20 and 25 have LCM 100. 3/20 = 15/100, 18/25 = 72/100. So 18/25 is larger, so more likely from the second bag. But the question first asks for the probability of the second bag as a fraction. So the fraction is 216/300 simplified. Wait, maybe I miscalculated the simplification. Wait, 216 ÷ 12 = 18, 300 ÷ 12 = 25. Wait, 18/25 is 0.72, and 3/20 is 0.15. So yes, 18/25 is correct for the second bag's probability. But the first part of the question (the first bag) has 3/20, but the user's image shows "as a fraction is [ ]" for maybe the second bag? Wait, the image says: "Suppose another bag has 300 letter tiles in it and 216 of the tiles are the letter B. Write the probability of picking a tile that is the letter B as a fraction and as a... From which bag are you more likely to pick a tile that is the letter B? as a fraction is [ ]." So we need to find the probability for the second bag as a fraction. So following the steps:

Number of B tiles = 216, total tiles = 300. Probability = 216/300. Simplify: divide numerator and denominator by 12: 216 ÷ 12 = 18, 300 ÷ 12 = 25. So 18/25. Wait, but 216 ÷ 12 is 18? 12×18 = 216, yes. 300 ÷ 12 = 25. So the simplified fraction is 18/25. Wait, but let's check again: 216 and 300. Let's divide numerator and denominator by 6 first: 216 ÷ 6 = 36, 300 ÷ 6 = 50. Then divide by 2: 36 ÷ 2 = 18, 50 ÷ 2 = 25. Same result. So the probability as a fraction is 18/25.

Answer:

\(\frac{18}{25}\)