Consider the experiment depicted by the Venn diagram, with the sample space S co

Question

Consider the experiment depicted by the Venn diagram, with the sample space S containing five sample points. The sample points are assigned the probabilities PE1)-0.2, P(E2) -0.2, P(E3) -0.1, PE4)-0.3, and P(E)0.2. Complete parts a through c a. Calculate P(A), P(B), and P(AnB) P(A)= (Type an integer or a decimal.) PB)- P(B)Type an integer or a decimal) P(ANB)-(Type an integer or a decimal.) b. Suppose event A has occurred, so that the reduced sample space consists of the three sample points in A namely, E1-E2, and E3 Use the formula for conditional probability to adjust the probabilities of these three sample points for the knowledge that A has occurred [that is, P(E IA). Find the ratio of the conditional probabilities to verify that they are in the same proportion to one another as the original sample point probabilities Calculate P(E,A) PE2IA), and P(E3IA). (Type an integer or a decimal.) points in A-namely. E E2 and E. Use the formula for PE 1 IA)= , P(EJA,- , Pf,A+ (Type integers or decimals.)

Explanation / Answer

a)P(A) =P(E1)+P(E2)+P(E3) =0.2+0.2+0.1=0.5

P(B) =P(E2)+P(E3)+P(E5) =0.2+0.1+0.2=0.5

P(AnB)=P(E2)+P(E3) =0.2+0.1=0.3

b)

P(E1|A) =0.2/0.5=0.4

P(E2|A)=0.2/0.5=0.4

P(E3|A)=0.1/0.5=0.2

P(E1) to P(E2) to P(E3) =2:2:1

P(E1|A) to P(E2|A) to P(E3|A) =2:2:1

c)

P(B|A) =0.3/0.5=0.6

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