Question

1. trisha trains guide dogs to assist people with visual impairments. trisha starts training the dogs when they are very young puppies. of the 46 puppies she worked with over the year, 11 of them did not complete the training.

a) what is the probability that the next puppy she trains will graduate, expressed as a percent? 1
b) if trisha trains 70 dogs next year, how many could she expect to graduate? 2

1. express the fraction $\frac{3}{5}$ as odds.
2. if the odds in favor of you failing a test is 1:6, what is the probability that you will pass the test?

Explanation:

Step1: Calculate number of graduated puppies

The number of puppies that graduated out of 46 is $46 - 11=35$.

Step2: Calculate probability of graduation for a single puppy

The probability $P$ that a puppy graduates is $\frac{35}{46}$. To convert to a percentage, we calculate $\frac{35}{46}\times100\approx76.1\%$.

Step3: Calculate expected number of graduates for 70 dogs

The expected number of graduates $E$ out of 70 dogs is found by multiplying the probability of graduation by the number of dogs. So $E=\frac{35}{46}\times70=\frac{2450}{46}\approx53.3\approx53$ (rounded to the nearest whole - number).

Step4: Express $\frac{3}{5}$ as odds

If the probability of an event is $\frac{3}{5}$, then the probability of the non - event is $1-\frac{3}{5}=\frac{2}{5}$. The odds in favor of the event is $\frac{\frac{3}{5}}{\frac{2}{5}}=\frac{3}{2}$, or $3:2$.

Step5: Calculate probability of passing given odds of failing

If the odds in favor of failing is $1:6$, then the probability of failing is $\frac{1}{1 + 6}=\frac{1}{7}$. So the probability of passing is $1-\frac{1}{7}=\frac{6}{7}$.

Answer:

a) Approximately $76.1\%$
b) 53

1. $3:2$
2. $\frac{6}{7}$