QUESTIONS 4 AND 5 ARE BASED ON THE FOLLOWING FIGURE,

13

. (Sub-tract

¹²

52

from 1.)An SAT probability problem might involve the probability of two independent events both occurring. Twoevents are “independent” if neither event affects the probability that the other will occur. Here are two generalsituations:* The random selection of one object from each of two groups (for example, the outcome of throwing a pair ofdice)* The random selection of one object from a group, then replacing it and selecting again (as in a “second round”or “another turn” of a game)To determine the probability of two independent events both occurring, multiply individual probabilities.Example:If you randomly select one letter from each of two sets: {A,B} and {C,D,E}, what is the probabilityof selecting A and C?Solution:The correct answer is

¹

₆

. The probability of selecting A from the set {A,B} is

¹

₂

, while theprobability of selecting C from the set {C,D,E} is

¹

₃

. Hence, the probability of selecting A and C is

1

2

×

3

, or

¹

₆

.An SAT probability problem might be accompanied by a geometry figure or other figure that provides a visualdisplay of the possibilities from which you are to calculate a probability.If a point is selected at random from the circular region shown above, what is the probability thatthe point will lie in a shaded portion of the circle?The correct answer is .25 (or

¹

₄

). The angles opposite each of the three 45° angles identified in thefigure must also measure 45° each. Given a total of 360° in a circle, all of the eight small anglesformed at the circle’s center measure 45°, and hence all eight segments of the circle are congruent.The two shaded segments comprise

²

₈

, or

¹

₄

(.25) of the circle’s area. The probability of selecting apoint at random in a shaded area is also

¹

₄

(or .25).