There are two bags each containing red balls and yellow balls. Bag A contains 1 red and 4 yellow balls. Bag B contains 3 red and 13 yellow balls. Alva says that if we choose one bag and draw one ball from that bag you should always choose bag B if you are trying to draw a red ball because it has more red balls than bag A.
P(red in A) = 1/5
P(red in B) = 3/16
To compare, change to decimals.
Desmond? As in Desmond Jenkins?
To determine if Alva's statement is correct, we need to compare the probabilities of drawing a red ball from each bag. Let's calculate the probabilities step-by-step.
Step 1: Find the total number of balls in each bag
- Bag A: 1 red ball + 4 yellow balls = 5 balls
- Bag B: 3 red balls + 13 yellow balls = 16 balls
Step 2: Calculate the probabilities of drawing a red ball from each bag
- Bag A: The probability of drawing a red ball from Bag A is given by the ratio of the number of red balls to the total number of balls in that bag.
Probability of drawing a red ball from Bag A = (1 red ball) / (5 total balls) = 1/5 = 0.2 or 20%
- Bag B: The probability of drawing a red ball from Bag B is also given by the ratio of the number of red balls to the total number of balls in that bag.
Probability of drawing a red ball from Bag B = (3 red balls) / (16 total balls) = 3/16 = 0.1875 or 18.75%
Step 3: Compare the probabilities
- The probability of drawing a red ball from Bag A is 0.2 (20%).
- The probability of drawing a red ball from Bag B is 0.1875 (18.75%).
Conclusion: The probability of drawing a red ball from Bag A is slightly higher than the probability of drawing a red ball from Bag B. Therefore, Alva's statement is incorrect. Bag A may be a better choice if you are trying to draw a red ball.
To determine whether Alva's statement is correct, we need to compare the probability of drawing a red ball from each bag.
Let's start by calculating the probability of drawing a red ball from Bag A. The total number of balls in Bag A is 1 (red) + 4 (yellow) = 5. Therefore, the probability of drawing a red ball is 1 red ball / 5 total balls = 1/5.
Next, let's calculate the probability of drawing a red ball from Bag B. Bag B contains 3 red balls and 13 yellow balls, so the total number of balls in Bag B is 3 (red) + 13 (yellow) = 16. Hence, the probability of drawing a red ball is 3 red balls / 16 total balls = 3/16.
Comparing the probabilities, we can see that the probability of drawing a red ball from Bag A is greater than the probability of drawing a red ball from Bag B (1/5 > 3/16). Therefore, Alva's statement is incorrect. Bag A has a higher probability of drawing a red ball than Bag B.
In conclusion, if you are trying to draw a red ball, you should choose Bag A rather than Bag B as it has a higher probability of obtaining a red ball.