Answer to Question #165058 in Statistics and Probability for mandeep ka

Question

. Eight vitamin and six sugar tablets identical in appearance are in a box. One tablet is taken at random and given to Person A. A tablet is then selected and given to Person B. What is the probability that

a.

Person A was given a vitamin tablet?

b.

Person B was given a sugar tablet given that Person A was given a vitamin tablet?

c.

neither was given vitamin tablets?

d.

both were given vitamin tablets?

e.

Person A was given a sugar tablet and Person B was given a vitamin tablet?

f.

Person A was given a vitamin tablet and Person B was given a sugar tablet?

 

Answer 1

1. Number of cases favorable for the event is equal to 8, because there are 8 vitamins. The number of total outcomes is equal to 8+6=14. So the probability is 8/14 = 4/7
2. Number of cases favorable for the event is 6. The number of total outcomes is 16-1=15, because Person A was given one vitamin tablet.
3. Number of cases favorable for the event is 6*5 (6 variants for the first person, and 5 remaining variants for the second). The number of total outcomes is 14*13. The probability is (6*5)/(14*13) = 15/91.
4. Number of cases favorable for the event is 8*7 (8 variants for the first person, and 7 remaining variants for the second). The number of total outcomes is 14*13. The probability is (8*7)/(14*13) = 4/13.
5. Number of cases favorable for the event is 6*8 (6 variants for the first person, and 8 variants for the second). The number of total outcomes is 14*13. The probability is (8*6)/(14*13) = 24/91.
6. Number of cases favorable for the event is 8*6 (8 variants for the first person, and 6 variants for the second). The number of total outcomes is 14*13. The probability is (8*6)/(14*13) = 24/91.