Question

challenge suppose you have a bag with 100 letter tiles in it and 19 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 is \\(\frac{19}{100}\\). suppose another bag has 200 letter tiles in it and 12% 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 percent. from which bag are you more likely to pick a tile that is the letter b?\\(p(b)\\) as a fraction is \\(\square\\) (simplify your answer.)

Explanation:

Step1: Identify the number of favorable and total outcomes

The number of letter B tiles (favorable outcomes) is 120, and the total number of letter tiles (total outcomes) is 300.

Step2: Calculate the probability as a fraction

The probability \( P(B) \) is the number of favorable outcomes divided by the total number of outcomes, so \( P(B)=\frac{120}{300} \). Simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 60. \( \frac{120\div60}{300\div60}=\frac{2}{5} \).

Step3: Calculate the probability as a percent

To convert the fraction \( \frac{2}{5} \) to a percent, multiply it by 100. \( \frac{2}{5}\times100 = 40\% \).

Step4: Compare the probabilities from both bags

The first bag has a probability of \( \frac{19}{100}=0.19 \) or 19%, and the second bag has a probability of 40%. Since 40% > 19%, we are more likely to pick a B tile from the second bag (with 300 tiles).

Answer:

• \( P(B) \) as a fraction: \( \boldsymbol{\frac{2}{5}} \)
• \( P(B) \) as a percent: \( \boldsymbol{40\%} \)
• More likely from the bag with 300 letter tiles (the second bag described).