Question

There are two traffic lights on Darlene's route from home to work. Let e denote the event that Darlene must stop at the first light, and define the event Fin a similar manner for the second light. Suppose that P(E) = 0.3, P(F) = 0.4, and P(EN F) = 0.13. (a) What is the probability that Darlene must stop at at least one light; that is, what is the probability of the event P(EU F)? (b) What is the probability that Darlene doesn't have to stop at either light? (c) What is the probability that Darlene must stop at exactly one of the two lights? (d) What is the probability that Darlene must stop just at the first light? (Hint: How is the probability of this event related to P(E) and P(En F)? A Venn diagram might help.)

Answer 1

E and Here tuo Events and I are defined as Ey denote the event that Darlene must stop at Ist light » similar for the fland ligut and Here it is given that PE=0:3; PE) - OR PLENF) = 0:13

P[ parlene must stup at exactly one of two light) PCE). PCA) + PCE). PCA) – REJ.(PCF). J + PCF):[[ PFIJ = L-0:3) * 0.4+ 0.3x11-04 0.7 x o.qt 0.3 xoit 0:28 to 18 z O: 46 2 P parlene must stop at exactly one of two light) = 0:46 d) Pl Darlene must stop just at Ist ligrit) PCE – PLENF) 0.3-0.13 -0.17 =) P[parlene must shop just at 1st light] = 0.17 TO