Question

E and F are mutually exclusive events. P(E) = 0.4; P(F) = 0.5. Find P(E|F). 41. J and K are independent events. P(JĮK) = 0.3. Find P()). 42. U and V are mutually exclusive events. P(U) = 0.26; P(V) = 0.37. Find: a. P(U AND V) = b. P(UV) = C. P(U OR V) =

Answer 1

Mutually exclusive events have a joint probability of zero, leading to P(E|F) = 0, while for independent events, the joint probability is the product of their individual probabilities. The probability of the union of mutually exclusive events is the sum of their individual probabilities.

Step-by-step explanation:

Calculating Probabilities of Independent and Mutually Exclusive Events

E and F are mutually exclusive events, which means that the occurrence of one event excludes the possibility of the other occurring. Therefore, the probability of E given F, P(E|F), is 0, as they cannot occur together.

For independent events J and K, the probability of J given K is simply the probability of J, P(J), since their occurrence is not affected by each other. If the probability of both J and K occurring together, P(JK), is 0.3 and they are independent, P(J) is divided by P(K) to find P(J).

With mutually exclusive events U and V, by definition, P(U AND V) is 0. The combined probability, or P(U OR V), is the sum of the individual probabilities, P(U) + P(V), as they cannot occur together.

The probability of independent events can be found using the multiplication rule, which states that P(J AND K) equals P(J) multiplied by P(K). Similarly, the probability of mutually exclusive events does not require any shared outcomes, therefore P(U AND V) = 0 and their union, P(U OR V), is simply the sum of their individual probabilities.