a)Suppose events E and F are mutually exclusive with P(E)= 0.15 and P(F)= 0.75. (i) What is the value of intersection P(E) and P(F)? ii) What is the value of P(E or F)? iii) If event E and F are independent, what is the value of P(E and F)? b) Suppose that for events A and B, P(A) = 0.24, and P(B)= 0.24, and P(A or B)= 0.48.

(d) P(N and W)     P(M and W)   (e) P(N or M). Are the events N = no reaction and M = mild reaction mutually exclusive? Explain. No. P(N or M) ≠ 0. No. P(N and M) ≠ 0.     Yes. P(N and M) = 0. Yes. P(N or M) = 0. (f) Are the events N = no reaction and W = washing oil off within 5 minutes independent? Explain. No. P(N and W) = P(N) · P(W). Yes. P(N and W) ≠ P(N) · P(W).     No. P(N and W) ≠ P(N) · P(W). Yes. P(N and W) = P(N) · P(W).

14. Event A and Event B are dependent. 21 a) P(B)=; p(A and B) 200 P(B|A) = b) P(B|A) = ; P(A and B) P(B) = 200

Let A and B be two events with P(A and Bc) = 1. Find P(B). Recall that Bc denotes the complement of the event B.

1. Events A and B are mutually exclusive with P(A) = 0.280 and P(A or B) = 0.740 a) P(B)= b) P(Not A)= c) P(A and B)=

4. Let A und B be two events such that: P(A)=0.48. P(B)=0.67 and P(AnB)=0.22 Then P(AUB) = a) 0.55 b) 0.93 c) 0.26 d) 0.87

1). If three events, A, B, and C, are such that P(A) = 0.5, P(B) = 0.3, P(AUC) = 0.65 and P(An B)= 0.1, Find the following: a). P(A/B) b). P (AUB) c). For what value of P(C) are A and C independent?