Final answer:
The individual probabilities for drawing a blue and white counter are 0.26 and 0.39 respectively.
Step-by-step explanation:
The question asks to find the probability of drawing a blue and white counter from a bag containing counters of only these two colors and red, with a given probability of drawing a red counter.
We are given the probability of getting red is 0.35, and the ratio of blue to white counters is 2:3.
To find the probability of getting a blue or white counter, we first subtract the probability of drawing a red counter from 1, which represents the total probability.
This gives us the combined probability of drawing either a blue or white counter. The probability of drawing a blue counter (P(Blue)) is then this combined probability multiplied by the proportion of blue counters relative to the total number of blue and white counters.
Similarly, the probability of drawing a white counter (P(White)) is the combined probability multiplied by the proportion of white counters.
First, we calculate the total probability for blue and white counters:
P(Blue or White) = 1 - P(Red)
= 1 - 0.35
= 0.65
Next, we determine the proportions for blue and white:
- Ratio of blue to white = 2:3
- Total parts = 2 + 3 = 5
- P(Blue) = (2/5) × P(Blue or White) = (2/5) × 0.65
- P(White) = (3/5) × P(Blue or White) = (3/5) × 0.65
Therefore:
- P(Blue) = 0.26
- P(White) = 0.39