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in a bag there are only red counters, blue counters and white counters, a counter is taken at random, the probability of getting red is 0.35, the number of blue counters : the number of white counters = 2 : 3, find the probability of getting a blue and white counter

User Darscan
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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
User Jasper Bernales
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