Complete question:
A market analyst is hired to provide information on the type of customers who shop at a particular store. A random survey is taken of 100 shoppers at this store. Of these 100, 73 are women. The shoppers The data is summarized below. we grouped in three age categories, under 30, 30 up to 50 and 50 and over. Women under 30 are 30, Men under 30 are 8 Women 30 to 50 are 25 and Men are 14 Women 50 and over are 18 and Men are 5.
Let W be the event that a randomly selected shopper is a woman. Let A be the event that a randomly selected shopper is under 30. a.) Find the probability of W. W (women Shoppers) = Find the probability of A. b.) Find the probability of A and W. c.) P (A and W) (Shoppers) d.) Find the probability of A or W. P(A or W) (Shoppers) e.) Find the probability of A given W
Answer:
A) P(W) = 73/100; B) P(A) = 38/ 100 C) 30 / 100
D) 81/100 E) 30/73
Step-by-step explanation:
- - - - - - - - Women Men Total
Under 30 - - - 30 - - - 8 - - 38
30 to 50 - - - - 25 - - 14 - - 39
50 & over - - - 18 - - - 5 - - -23
Totals - - - - - - 73 - - -27 - - 100
Recall:
Probability : P= (required outcome / Total possible outcomes)
A) probability of women shoppers: P(W)
Number of women shoppers = 73; total shoppers = 100
P(W) = 73/100
B) Probability of under 30: P(A)
= number of shoppers under 30 = 38
Tital number of shoppers = 100
P(A) = 38/ 100
C) probability of A and W; This is the probability that the selected person is a woman and under 30.
(W n A) = 30
= 30 / 100
D) probability of A or W:
P(A) + P(W) - P(A n W) :
(38 / 100 + 73 / 100 - 30 / 100) = (38+73-30) /100
= 81/100
E) probability of A given W:
P(A n W) / P(W) = 30/73
1) The outcomes for rolling two dice, the sample space, is as follows:
(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)
There are 36 outcomes in the sample space.
2) The ways to roll an odd sum when rolling two dice are:
(1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (3, 6), (4, 1), (4, 3), (4, 5), (5, 2), (5, 4), (5, 6), (6, 1), (6, 3), (6, 5). There are 18 outcomes in this event.
3) The probability of rolling an odd sum is 18/36 = 1/2 = 0.5
