Question

Consider A and B are independent events, and P(A) = 0.34 and P(B) = 0.74. Fill in the missingprobabilities on the Venn Diagram below.P(C)ABP(ΑΛΒ)A PAB) = 0.2516, PCA)=0.34,PB) = 0.74, PC)-0.1716BP(AB) = 0.2516, P(A)=0.34,P(B) = 0.74, PC) 0.4232C P(ACB) =0.2516 P(A)=0.0884,P(B) 0.4884. PC) 0.4232D P(AB) = 0.2516, P(A)=0.0884,PYB) -0.4884. PIC) 0.1716ООООооо

Answer 1

Since A and B are independents events, we can use the formulas:

$\begin{gathered} P(A\cap B)=P(A)\cdot P(B) \\ P(A\cup B)=P(A)+P(B)-P(A\cap B) \end{gathered}$

So, calculating the probability of A and B, we have:

$\begin{gathered} P(A\cap B)=0.34\cdot0.74_{} \\ P(A\cap B)=0.2516 \end{gathered}$

C is the complementary event of A or B, so we have the following:

$\begin{gathered} P(C)=1-P(A\cup B) \\ P(C)=1-(P(A)+P(B)-P(A\cap B))_{} \\ P(C)=1-(0.34+0.74-0.2516) \\ P(C)=1-0.8284 \\ P(C)=0.1716 \end{gathered}$

So the correct option is A.