Question

Question 3 A study of workers earning minimum wage were grouped into various categories, which can be interpreted as events when a worker is selected at random. Considering the following events: E: worker is under 20 years of age F: worker is white G: worker is female Describe the following events in words • E’ • F ꓵ G’ • E ꓴ G Question 4 if a single card is drawn from an ordinary deck of cards, find the probability it will be a red or a face card. (Face cards are Jack, Queen, and King) Question 5 Supposed two fair die are rolled. Find the probability the first die shows a two or the sum of the result is six or seven. Question 6 If two fair die are rolled find the probability that the sum of the numbers rolled is greater than three. (Be careful of the phrase greater than). please show work or give explnation so i can try and figure out how to do the problems

Answer 1

3.

E’ = worker is over 20 years of age

F ꓵ G’ = worker is male white

E ꓴ G = worker is under 20 years of age or female

4.

Number of face or red cards in a ordinary deck of cards = Number of face cards + Number of red cards - Number of red and face cards = 12 + 26 - 6 = 32

probability it will be a red or a face card = 32 / 52 = 0.6153846

5.

Probability the first die shows a two = 1/6

Sample space of roll of two fair dice where the first die shows a two and the sum of the result is six or seven

= (2, 4) , (2.5)

Probability the first die shows a two and the sum of the result is six or seven = 2/36

Sample space of sum of the result is six or seven = (1, 5) (2, 4) (3, 3) (4, 2) (5, 1)  (1, 6) (2, 5) (3, 4) (4, 3) (5, 2) (6,1) = 11

Probability the sum of the result is six or seven = 11/36

Probability the first die shows a two or the sum of the result is six or seven = Probability the first die shows a two + Probability the sum of the result is six or seven - Probability the first die shows a two and the sum of the result is six or seven

= (1/6) + (11/36) - (2/36)

= 15/36

6.

Sample space of sum of the result is less than or equal to three = (1,1) (1, 2) (2, 1)

probability that the sum of the numbers rolled is greater than three = 1 - probability that the sum of the numbers rolled is less than or equal to three

= 1 - 3/36

= 33/36

= 11/12