Question

In: Math

Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities...

Researchers watched groups of dolphins off the coast of Ireland in 1998 to determine what activities the dolphins partake in at certain times of the day. The numbers in the Table below represent the number of groups of dolphins that took part in an activity at certain times of days. In Excel

               

Activity

Morning

Noon

Afternoon

Evening

Total

Travel

6

6

14

13

39

Feed

28

4

0

56

88

Social

38

5

9

10

62

Total

72

15

23

79

189

  1. Calculate the probability (in reduced fraction form) that a dolphin group is involved with travel.
  2. Calculate the probability (in reduced fraction form) that a dolphin group is around in the morning.
  3. Calculate the probability (in reduced fraction form) that a dolphin group is involved with travel, given that it is morning.
  4. Calculate the probability (in reduced fraction form) that a dolphin group is around in the morning, given that it is socializing.
  5. Calculate the probability (in reduced fraction form) that a dolphin group is around in the afternoon, given that it is feeding.
  6. Calculate the probability (in reduced fraction form) that a dolphin group is either around in the evening or is feeding.

Solutions

Expert Solution

a)                  
required probability = 39/189 =13/63                  
                  
b)                  
required probability = 72/189 = 8/21                  
                  
c)                  
P(travel | morning) = 6/72 = 1/12                  
                  
                  
d)                  
P(morning | socializing) = 38/62 = 19/31                  
                  
                  
e)                  
P(afternoon | feeding) = 0                  
                  
                  
f)                  
P(evening or feeding) = (79+88-56)/189=111/189 = 37/63                  


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