Question

In a survey of 120 passengers, an airline found that 48 enjoyed
cool drinks with their meals, 78 enjoyed coffee and 66 enjoyed
tea. In addition 36 enjoyed any given pair of these beverages and
24 passengers enjoyed them all. If two passengers are selected
at random, what is the probability that they both want only tea
with their meals?

Answer 1

Given : In a survey of 120 passengers, an airline found that 48 enjoyed

cool drinks with their meals, 78 enjoyed coffee and 66 enjoyed

tea. In addition 36 enjoyed any given pair of these beverages and

24 passengers enjoyed them all.

To Find :  two passengers are selected  at random, what is the probability that they both want only tea  with their meals?

Solution:

Total = 120

Cool Drink  D = 48

Coffee C = 78

Tea T =  66

D∩T  =  36

D∩C = 36

C∩T  = 36

D∩T∩C  =  24

Only Tea  = T - D∩T  - C∩T  + D∩T∩C

= 66 - 36 - 36  + 24

= 18

probability that they both want only tea  with their meals

= ¹⁸C₂ / ¹²⁰C₂

= 18 * 17 / 120 * 119

=  3/140

 3/140 is the probability that they both want only tea  with their meals

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