Question

Diamond has four phone cases. Two phone cases have a pop socket while the other two do not. Every morning, Diamond closes her eyes and randomly selects one phone case to use for the day.

Part A: What is the probability that Diamond selects a phone case with a pop socket?

Part B: One morning, before Diamond wakes up, her little sister borrows one of the cases with a pop socket. Given that Diamond's sister has taken one of the pop socket phone cases, what is the probability that Diamond randomly selects a phone case with a pop socket? Write your answer as a fraction

Answer 1

Diamond has a 1/2 probability of selecting a phone case with a pop socket initially, and if her sister borrows one, the probability becomes 1/3.

Step-by-step explanation:

The probability that Diamond selects a phone case with a pop socket (Part A) can be calculated by dividing the number of cases with a pop socket by the total number of cases. As there are 2 cases with a pop socket and 4 cases in total, the probability is 2/4 which simplifies to 1/2 or 50%.

For Part B, if one phone case with a pop socket is borrowed by Diamond's sister, there are now only 3 cases left to choose from, and only 1 of them has a pop socket. The probability in this situation is 1/3.