### Find the probability that for family with four children

Assignment Help Mathematics
##### Reference no: EM132607618

Question 1.
A survey obtained the following results: 42 people had been to the Moon, 57 had been to Mars, 52 had been to Venus, 17 had been to the Moon and Mars, 12 had been to the Moon and Venus, 7 had been to Mars and Venus, 4 had been to all three, and 18 had been to none of the three.
(a) How many people were interviewed?
(b) How many people had only been to Mars?
(c) How many people had only been to one of the three places? Hint: Use a Venn diagram.

Question 2.
(a) A pair of identical fair dice is rolled. What is the probability that the sum of the numbers is more than 6?
(b) A pair of identical fair dice is rolled. What is the probability that one of the numbers is more than 4?
(c) A pair of identical fair dice is rolled. What is the probability that the sum of the numbers is more than 6, if it is known that one of the numbers is a 4?
(d) A pair of fair dice, one red and one green, is rolled. What is the probability that the sum of the numbers is more than 6, if it is known that the red one shows a 4?

Question 3.
Assume that the probability of a boy being born is the same as the probability of a girl being born.
(a) Find the probability that for family with four children, the two oldest children are girls.
(b) Find the probability that for family with four children, exactly two of the children are boys.
(c) Find the probability that for family with four children, at least two of the children are boys.

Question 4.
A survey shows that 80% of a population has been vaccinated against the flu, but 5% of the vaccinated population gets the flu anyway. In total 10% of the population gets the flu. Let V be the event that a randomly selected person in the population has been vaccinated and Fthe event that a randomly selected person in the population gets the flu.
(a) Present the information using either a Venn diagram or a table or both.
(b) Estimate the following probabilities and describe the probabilities in words.
• P(F')
• F(F∩V)
• P(F∩V')
• P(F|V)
• P(V|F)
(c) Does this survey provide evidence that the events F and V are not independent? Give a reason for your answer.
(d) Which conditional probabilities will you calculate to explain whether vaccination should be encouraged?

Question 5.

Three horses A, B and C are going to race against each other. The probability that A wins is 1/5. The probability that B wins is 1/2

(a) What is the probability that C wins?
(b) What are the odds that C wins?
(c) Are the events A wins and B wins mutually exclusive? Give a reason for your answer.
(d) Are the events A wins and B wins independent? Give a reason for your answer.

Question 6.
HTML colours are represented by 6-digit hexadecimal codes.

Each digit can take on 1 of 16 values: 0, 1, 2, . . . , A, B, C, D, E, F.
(a) How many different colours can be represented?
(b) There are three types of pure colours: pure red (represented by xy0000); pure green (represented by 00xy00); pure blue (represented by 0000.4. How many pure colours are possible?
(c) Grayscale shades are represented by codes xyxyxy consisting of a repeated pair of digits. How many grayscale shades are possible?
(d) Some monitors could only display colours with codes consisting of three pairs of repeating digits: xxyyzz. How many colours could these monitors display?

Question 7.
There are 65 handmade music boxes, four of which are made by an assistant and 61 are made by technicians. Ten randomly selected music boxes are tested.
(a) In how many ways can ten music boxes be selected from the 65 music boxes? Give the answer in factorial notation.
(b) What is the probability that at least one music box made by the assistant is selected?

Question 8.
Three marbles are removed from a box that contains 4 red and 8 green marbles.
(a) What is the probability that all three are red?
(b) What is the probability that all three are of the same colour?
(c) What is the probability that at least 1 marble is red?

Question 9.
Assume that E and F are two mutually exclusive events. Will the events E' and P be mutually exclusive? Give a reason for your answer.

### Write a Review

#### Question regarding lipschitz functions

Show that if f:A->R is Lipschitz then it is uniformly continuous on A. Is the converse statement true? Are all uniformly continuous functions necessarily Lipschitz?

#### How long should warranty provide follows normal distribution

In a random sample of 615 people, 72% said they would rather eat worms than take a Business Research Methods final exam. How confident can you be that between 70 and 74% of the general population feels this way?

#### Grocery store of selling a bottle of salad dressing

Assume that the marginal cost to a grocery store of selling a bottle of salad dressing to customers who present coupons versus those who don't is identical and equal to \$1.50. If the elasticity of demand of coupon holders is 5 versus 1.25 for other c..

#### Find the length of each segment

Find the length of each segment whose endpoints are (-8, -4) and (4,-8) , (6,4) (-5, 0)

#### Suggest about the range of work

What do your examples suggest about the range of work in the early Modernist period and its artists?

#### Define a set solution concept as given

A set solution concept for a family of bargaining games F is a function ? associating every bargaining game (S, d) in F with a subset of S. Let f : R4 → R be a function. Define a set solution concept ? as given.

#### How much should be set aside today for trip

Shirley Riddle received a \$10,000 gift from her mother and plans a minor renovation to her home. She also plans to make an investment for one year.

#### Construct a 95% confidence interval for the mean

Suppose Motorola wishes to estimate the mean talk time for its V505 camera phone before the battery must be recharged. In a random sample of 50 phones, the sample mean talk time was 347 minutes.

#### Two angles are supplementary the measure of the smaller

two angles are supplementary. the measure of the smaller angleis one-half the measure of the largeer angle. find the

#### What is the mode of the following numbers

If a student scored 74 points on a test where the mean score was 80 and the standard deviation was 6.  What was the student's z-score?

#### Find the sum of the numbers appearing uppermost on die

Determine whether the given experiment has a sample space with equally likely outcomes.

#### Find the temperature of the soup

Find the temperature of the soup 16 minutes after it is placed in the room. (Round to the nearest degree.) 