Final answer:
To find the probability of selecting two female action figures without replacement when Tamlin has 2 more females than males, we multiply the probability of selecting a female on the first draw with the probability of selecting a female on the second draw, after one female has been removed.
Step-by-step explanation:
The student has asked to simplify the expression that represents the probability of randomly selecting two female action figures from Tamlin's collection, knowing that Tamlin has 2 more female action figures than male action figures, and not replacing the first action figure chosen. Let x represent the number of male action figures Tamlin has. Therefore, Tamlin has x + 2 female action figures.
The probability that the first action figure chosen is female is (x + 2) divided by the total number of action figures, which is x + (x + 2) or (2x + 2). The probability that the second action figure chosen is also female, after not replacing the first, is (x + 1) (since one female has already been taken out) divided by the total minus one, which is (2x + 1).
The combined probability of both events occurring is the product of the two separate probabilities:
- Probability of first female action figure: (x + 2) / (2x + 2)
- Probability of second female action figure: (x + 1) / (2x + 1)
- Combined probability: [(x + 2) / (2x + 2)] × [(x + 1) / (2x + 1)]
Upon simplifying the expression, we will cancel common factors and get the simplified probability expression for selecting two female action figures without replacement.