# Suppose that when the weather is rainy the probability that Lily goes to her outdoor baseball practice is 0.1, but when it's not raining the probability is 0.9. The probability it will rain tomorrow is 0.3. Determine the probability that She will go to her baseball practice tomorrow.

Question
Probability
Suppose that when the weather is rainy the probability that Lily goes to her outdoor baseball practice is 0.1, but when it's not raining the probability is 0.9. The probability it will rain tomorrow is 0.3. Determine the probability that She will go to her baseball practice tomorrow.

2020-11-11
Let A denote the event that Lily goes to practice, and let B denote the event that rains. Then
$$\displaystyle{P}{\left({A}\right)}={P}{\left({A}{\mid}{B}\right)}{P}{\left({B}\right)}+{P}{\left({A}{\mid}{B}^{{c}}\right)}{P}{\left({B}^{{c}}\right)}$$
(B* is the complementary event of B — here it is the event that it does not rain). Also,
$$\displaystyle{P}{\left({B}\right)}={0.3}\Rightarrow{P}{\left({B}^{{c}}\right)}={1}-{P}{\left({B}\right)}={0.7}$$
Also, we are given that
$$\displaystyle{P}{\left({A}{\mid}{B}\right)}={0.1}$$
$$\displaystyle{P}{\left({A}{\mid}{B}^{{c}}\right)}={0.9}$$
Therefore,
$$\displaystyle{P}{\left({A}\right)}={0.1}\cdot{0.3}+{0.9}\cdot{0.7}={0.66}$$

### Relevant Questions

If there is a 25% chance that it will rain on any given day in Seattle, find the probability that it will rain for three consecutive days.
Energy is conventionally measured in Calories as well as in joules.One Calorie in nutrition is 1 kilocalorie, which we define inChapter 11 as 1 kcal = 4,186 J. Metabolizing 1 gram of fat canrelease 9.00 kcal. A student decides to try to lose weight byexercising. She plans to run up and down the stairs in a footballstadium as fast as she can and as many times as necessary. Is thisin itself a practical way to lose weight?
yes
no
To evaluate the program, suppose she runs up a flight of90 steps, each 0.150 m high, in67.0 s. For simplicity, ignore theenergy she uses in coming down (which is small). Assume that atypical efficiency for human muscles is 20.0%. This means that whenyour body converts 100 J from metabolizing fat, 20 J goes intodoing mechanical work (here, climbing stairs). The remainder goesinto internal energy. Assume the student's mass is 57.0 kg.
(a) How many times must she run the flight ofstairs to lose 1 pound of fat?
(b) What is her average power output, in watts and in horsepower,as she is running up the stairs?
W
hp
You ask a neighbor to water a sickly plant while you are on vacation. Without water the plant will die with probability 0.85. With water it will die with probability 0.5. You are 90 % certain the neighbor will remember to water the plant. You come back from the vacation and the plant is dead. What is the probability that the plant died because neighbor forgot to water it?
Charlie and Clare are playing a number-guessing game. Charlie picked two numbers between 1 and 5. To win the game, Clare must guess both his numbers in three lines. Her guesses, simulated using a random-number generator are shown in the table. If Charlie's numbers are 1 and 3, what is the experimental probability that Clare won?
It is estimated that aproximately $$\displaystyle{8.36}\%$$ Americans are afflicted with Diabetes .
Suppose that a ceratin diagnostic evaluation for diabetes will correctly diagnose $$\displaystyle{94.5}\%$$ of all adults over 40 with diabetes as having the disease and incorrectly diagnoses $$\displaystyle{2}\%$$ of all adults over 40 without diabetes as having the disease .
1) Find the probability that a randamly selected adult over 40 doesn't have diabetes and is diagnosed as having diabetes ( such diagnoses are called "false positives").
2) Find the probability that a randomly selected adult of 40 is diagnosed as not having diabetes.
3) Find the probability that a randomly selected adult over 40 actually has diabetes , given that he/she is diagnosed as not having diabetes (such diagnoses are called "false negatives").
Note: It will be helpful to first draw an appropriate tree diagram modeling the situation.
Fruit Flles An experiment with fruit flies involves one parent with notmal wings and ooe parent with vestigial wings. When these parents have an of$$\displaystyle\frac{{3}}{{4}}$$ probabulty that the of$$\displaystyle\frac{{1}}{{4}}/{4}$$ probability of vestigial wings. If the parents give birth to five of See answers (1)