Question

Consider randomly drawing two students without replacement from a class of 40 students in which 3 are left handed. Below is a tree diagram illustrating that the probability of selecting 2 left handed students is 1/260. Calculate the probabilities labeled on the tree diagram

Answer 1

Answer:

a. 3/40

b. 37/40

c. 2/39

d. 37/39

e. 3/39

h. 36/39

k. 1/260

m. 37/520

n. 37/520

w. 111/130

Step-by-step explanation:

First person:

a. 3/40

b. 37/40

_____

Second person:

left-handed branch of tree diagram: since the first person was left-handed, it means there is one less left-handed person, and one less person for the total

c. 2/39

d. 37/39

not left-handed branch of tree diagram: since the first person wasn't left-handed, there are still 3 left-handed people, and there is one less person for the total.

e. 3/39

h. 36/39

_____

for the final probabilities, just multiply along the tree branches:

k = a × c = 1/260

m = a × d = 37/520

n = b × e = 37/520

w = b × h = 111/130