Final answer:
The probability of event E or event F occurring, given P(E)=0.30, P(F)=0.55, and P(E and F)=0.15, is calculated using the addition rule and is found to be 0.70.
Step-by-step explanation:
The student has asked to find the probability of the event P(E or F) given that P(E)=0.30 and P(F)=0.55, and we are also given that P(E and F) = 0.15.The probability of event E or event F occurring, given P(E)=0.30, P(F)=0.55, and P(E and F)=0.15, is calculated using the addition rule and is found to be 0.70.
To find the probability of E or F, we use the addition rule of probability, which states that the probability of either event E or event F occurring is equal to the sum of the probabilities of each event occurring separately minus the probability of both events occurring together. This is expressed mathematically as:
P(E or F) = P(E) + P(F) - P(E and F)
Substituting the given values into the formula, we have:
P(E or F) = 0.30 + 0.55 - 0.15
P(E or F) = 0.85 - 0.15
P(E or F) = 0.70
Therefore, the probability that event E or event F will occur is 0.70.