4. The Probability Calculus - Restricted Disjunction Rule To calculate the probability that either of two events will occur when the events are mutually exclusive, use the restricted disjunction rule. Two events are mutually exclusive if they cannot both occur at the same time. To calculate the probability of either of two mutually exclusive events (A and B) occurring, according to the restricted disjunction rule, use the following formula: P(A or B) = P(A) + P(B) This formula tells you that the probability of either of two mutually exclusive events occurring is equal to the probability that event A occurs plus the probability that event B occurs. Because a disjunctive event permits a wider range of options, the probability that either of the two events takes place is greater than the probability that only one of the events takes place. This is the reason that the formula for the restricted disjunction rule consists of the addition of two probabilities. For example, the probability of drawing the ace of spades from a deck of 52 playing cards is 1/52. Likewise, the probability of drawing the queen of hearts from a deck of 52 playing cards is also 1/52. When drawing a single card from the deck, these two events are mutually exclusive because they cannot both occur. Therefore, according to the restricted disjunction rule, the probability of drawing either the ace of spades or drawing the queen of hearts is equal to 1/52 + 1/52 = 2/52 = 1/26. Use the restricted disjunction rule to determine the probability of the two events (A and B). Indicate the probability for event A and the probability for event B. Then indicate the probability that either of the two events occurs. Reduce fractional probabilities to the lowest whole numbers. Type your numeric answers into the spaces provided. If a glass jar contains 5 blue balls, 22 green balls, and 20 red balls, what is the probability of drawing either a blue ball (event A) or a green ball (event B) according to the restricted disjunction rule? What is the probability of event A (expressed as a fraction)? ':] / [: What is the probability of event B (expressed as a fraction)? ':] / [: What is the probability of either event A or event B occurring (expressed as a fraction)? D / E