Question

3) Consider the type and number of ducks. -1 bufflehead -2 blue-winged -2 red-winged Let’s assume that the probability of selecting any individual duck is equal. What is the probability of sampling the bufflehead? What is the probability of sampling a blue-winged teal? What is the probability of generating the following outcome (in this order): one cinnamon teal, one blue-winged teal, and the bufflehead?

follow up, 4) Using the above duck example, what is the probability of sampling either a cinnamon teal or the bufflehead? What is the probability of sampling a blue-winged teal or a cinnamon teal? What is the probability of sampling a duck?

Answer 1

Total number of Ducks = 5

Bufflehead = 1 ; P( bufflehead) = 1/5

Blue- winged = 2; P( Blue winged) = 2/5

Red- winged i.e, Cinnamon = 2; P( Cinnamon) = 2/5

* Here i am considering , red- winged as cinnamon teal, as there is no information about the cinnamon teal and no other use of red-winged teal. I guess i am right)

a)  P( bufflehead) = 1/5

b) P( Blue winged) = 2/5

c)P( one cinnamon teal, one blue-winged teal, and the bufflehead)

d)  probability (either a cinnamon teal or the bufflehead) = P( Cinnamon) + P( Bufflehead)

= (2/5) + (1/5)

= 3/5

= P( Cinnamon) * P( Blue- winged) * P( Bufflehead)

= ( 2/5) * ( 2/4) * ( 1/3) { considering without replacement}

= 1/15

d)P(  a blue-winged teal or a cinnamon teal ) = P( Blue- winged ) + P( Cinnamon)

= (2/5) + ( 2/5)

= 4/5

e) P( Duck) = 1