Answer:
a) The probability tree has been created below
b) The likelihood of selecting at least two women is 0.500
Step-by-step explanation:
Based on the information provided in the question;
a) The constructed probability tree is outlined as follows;
3 men, 3 women
↓
_______________________|________________________
↓ ↓ ↓ ↓
3 men 2 men 1 man 0 men
0 women 1 woman 2 women 3 women
b) The probability of having at least two women selected
p( at least two women would be selected) = P( there are 2 women out of 3 ) + P( there are 3 women out of 3 )
Thus,
p( at least two women would be selected) = C
³C₂ × ³C₁ / ⁶C₃ + ³C₃³C₀ / ⁶C₃
= 3!/(2!(3-2)!) × 3!/(1!(3-1)!) / 6!/(3!(6-3)!) + 3!/(3!(3-3)!) × 3!/(0!(3-0)!) / 6!/3!(6-3)!)
= 3 × 3 / 20 + 1 × 1 / 20
= 9/20 + 1/20
= 0.45 + 0.05
p( at least two women would be selected) = 0.500
Thus, the probability of selecting at least two women is 0.500
