Final answer:
The probability that x takes on a value greater than 2 is calculated by adding the probabilities for the states greater than 2, which is 0.20, assuming no probability for the unlisted state 4.
Step-by-step explanation:
The probability that x takes on a value greater than 2 in a nickel-cadmium (NiCd) battery is calculated by adding the probabilities of x taking on values strictly greater than 2. As given, we have the probabilities for the oxidation states (0, 2, 3, 4) and their corresponding probabilities (p, 0.23, 0.35, 0.20).
If we add the probabilities for the oxidation states greater than 2 (which are the states 3 and 4), we get 0.20 for state 3 (no information is provided for state 4), indicating that the answer could be incomplete as provided. In case there's an implied probability of 0 for state 4 (since it is not listed), the probability would simply be 0.20 for x > 2.