High school probability Uncovered: Discover the Secrets with Plainmath's Expert Help

Exposure of certain fruit fly population to an insecticide has produced 2 kinds of mutations. 20% have wing mutation. 15% have eye mutation and 5% have both. A fly is selected at random.
a) If it has wing mutation, what is the probability that, it also has the eye mutation?
b) If it has the eye mutation, what is the probability that it has also the wing mutation?
c) What is the probability that it has at least one of the mutations?

Here is the probability model for the blood type of a randomly chosed person in the United States.
$$\begin{array}{|ccccc|}\hline Bloodtype& O& A& B& AB\\ Probability& 0.53& 0.18& 0.01& 0.28\\ \hline\end{array}$$
What is the probability that a randomly chosen American does not have type O blood?

A restaurant menu lists seven entrée choices. Two of the entrée choices are vegetarian. One member of a couple chooses one entrée at random and then the other member chooses a different entrée at random. Consider the problem of calculating the probability that the couple choose vegetarian entrées.
- Can a binomial distribution be used for the solution of the above problem? Why or why not?
- What kind of probability distribution can be used to solve this problem?
- What is the probability that both members chose vegetarian entrées?

The probability that a vehicle entering the Luray Caverns has Canadian license plates is 0.19; the probability that it is a camper is 0.38; and the probability that it is a camper with Canadian license plates is 0.13. What is the probability that
(a) a camper entering the Luray Caverns has Canadian license plates?
(b) a vehicle with Canadian license plates entering the Luray Caverns is not a camper?
(c) a vehicle entering the Luray Caverns does not have Canadian plates or is not a camper?

The amount of time required for a mechanic to replace a clutch is normally distributed with mean 90 minutes and standard deviation of 15 minutes. A car is taken to the mechanic to have its clutch replaced.
a) Find the probability that the car will be ready in two hours.
b) Find the probability that the car will not be ready after 80 minutes.
c) Find the probability that the car is ready in between 85 to 95 minutes.

If ${\displaystyle P\left(A\right)=0.4}$, ${\displaystyle P\left(B\right)=0.5}$, and ${\displaystyle P(A\cap B)=0.3}$, find a. ${\displaystyle P(A\cup B)}$, b. ${\displaystyle P(A\cap B^{\prime })}$, and c. ${\displaystyle P(A^{\prime }\cup B^{\prime })}$.

if the probability of event A is ${\displaystyle \frac{3}{4}}$ and the probability of event B is 1/4 then the probability of both A and B occuring at the same time is
A)1 or absolute certainty
B) ${\displaystyle \frac{1}{2}}$
C) ${\displaystyle \frac{3}{16}}$
D) ${\displaystyle \frac{3}{4}}$
E) ${\displaystyle \frac{1}{4}}$

Sam and Allen have applied for scholarships. The probability that Sam gets a scholarship is 0.93. The probability that Allen gets a scholarship is 0.77. The probability they both get scholarships is 0.74.
(a) What is the probability that Sam gets a scholarship but Allen doesnt?

Uniaxial tensile tests were carried on a ceramic. The following strength values were obtained:
310, 380, 400, 415, 448, 455, 475, 489, 500, and 502.
a. Calculate the probability of survival or probability of failure for these data. What is the Weibull modulus? Also calculate the characteristic strength.
b. What is the tensile strength at ${\displaystyle 50\mathrm{\%}}$ survival probability? If the volume was increased three fold, what would be the new strength value at ${\displaystyle 50\mathrm{\%}}$ survival probability?

Use the formula for the probability of the complement of an event.
Two dice are tossed. What is the probability of getting a sum of at least 5? (Enter your probability as a fraction.)

A boat on the ocean is 4 mi from the nearest point on a straight shoreline; that point is 6 mi from a restaurant on the shore. A woman plans to row the boat straight to a point on the shore and then walk along the shore to the restaurant. a. If she walks at 3 mi/hr and rows at 2 mi/hr, at which point on the shore should she land to minimize the total travel time?
b. If she walks at 3 mi/hr, what is the minimum speed at which she must row so that the quickest way to the restaurant is to row directly (with no walking)?

Although it’s hard to be definitive in classifying people as right- or left-handed, some studies suggest that about 14% of people are left-handed. Since ${\displaystyle 0.14\times 0.14=0.0196}$ the Multiplication Rule might suggest that there’s about a 2% chance that a brother and a sister are both lefties. What’s wrong with that reasoning?

In a hospital, the probability of male births is 0.4.
a) What is the probability that the number of female births is 9 in the next 20 births?
b) What is the probability that the number of female births is less than 18 in the next 20 births?

The mean of a normal probability distribution is 60; the standard deviation is 5. a. About what percent of the observations lie between 55 and 65? b. About what percent of the observations lie between 50 and 70? c. About what percent of the observations lie between 45 and 75?

A pair of dice is rolled. The outcomes are summarized in the following table:
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5.1) (5,2) (5,3) (5.4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6.4) (6,5) (6,6)
1. Find the probability, that the sum is 11 (adding the two numbers will equal to 11). Give your answer as a decimal, rounded to two decimal digits.
2. Find the probability, that the sum is more than 10 (which means 11 or 12). Give your answer as a decimal, rounded to two decimal digits.
3. Find the probability, that the sum is 6 OR the sum is more than 10. Give your answer as a decimal, rounded to two decimal digits.

The following probability table is a breakdown of managers in four setors of economy:
$$\begin{array}{|ccccc|}\hline & Banking& Insurance& RealEstate& Manufacturing\\ Male& 0.12& 0.14& 0.13& 0.21\\ Female& 0.08& 0.06& 0.17& 0.09\\ \hline\end{array}$$
a) What is the probability that the selected manager is female?
b) What is the probability that the selected manager is female or in insurane business?
c) What is the probability that the selected manager is neither female nor in insurance business?

You are playing a game with your friend. You win with 55% probability, your friend 30%. There is no draw. You decide to play a series of games. What is your probability of winning the series if the player with
a) 5 wins?
b) 6 wins?

The following table provides a frequency distribution for the number of rooms in this​ countrys

Roll a fair die 10 times. What is the probability to get “six” twice? And, What is the probability to get “six” at least twice?

For a certain airline, there is a 75% probability that a given flight will depart on-time, an 80% probability of an on-time arrival, and a 60% probability of both an on-time departure and arrival.
What is the probability that this flight will either depart on-time or arrive on-time?
Is on-time arrival independent of on-time departure?