Questions: Given the following information, find the probability that a randomly selected dog will not be a golden retriever. Number of dogs who are poodles: 31, golden retrievers: 58 , beagles: 20, pues: 38 Given that there is a 22 % chance it will rain on any day, what is the probability that it will rain on the first day and be clear (not rain) on the next two days?

Solution Steps

To find the total number of dogs, we sum the number of each breed: \[ \text{Total dogs} = \text{Poodles} + \text{Golden Retrievers} + \text{Beagles} + \text{Pugs} = 31 + 58 + 20 + 38 = 147 \]

The probability \( P(GR) \) that a randomly selected dog is a golden retriever is calculated as: \[ P(GR) = \frac{\text{Number of Golden Retrievers}}{\text{Total Number of Dogs}} = \frac{58}{147} \approx 0.3946 \]

The probability \( P(NGR) \) that a randomly selected dog is not a golden retriever is: \[ P(NGR) = 1 - P(GR) = 1 - 0.3946 \approx 0.6054 \]

Given the probability of rain \( P(R) = 0.22 \) and the probability of it being clear \( P(C) = 1 - P(R) = 0.78 \), the probability that it will rain on the first day and be clear on the next two days is: \[ P(R \text{ on Day 1 and } C \text{ on Day 2 and Day 3}) = P(R) \cdot P(C) \cdot P(C) = 0.22 \cdot 0.78 \cdot 0.78 \approx 0.1338 \]

Final Answer