Question

If E1andE2 are two events such that P(E1)=0.5,P(E2)=0.3andP(E1andE2)=0.1, find (i) P(E1 or E2) (ii) P(E1 but not E2) (iii) P(E2 but not E1) (iv) P( neither E1 nor E2) Select the correct answer from above options

Answer 1

We have P(E1)=0.5,P(E2)=0.3andP(E1∩E2)=P(E1andE2)=0.1 . ∴P( ¯ E1 )={1-P(E1)}=(1-0.5)=0.5, and P( ¯ E2 )={1-P(E2)}=(1-0.3)=0.7. Thus, we have (i) P(E1 or E2)=P(E1∪E2) =P(E1)+P(E2)-P(E1∩E2) =(0.5+0.3-0.1)=0.7. (ii) P(E1 but not E2)=P(E1∩ ¯ E2 ) =P(E1)-P(E1∩E2) =(0.5-0.1)=0.4. (iii) P(E2 but not E1)=P(E2∩ ¯ E1 ) =P(E2)-P(E2∩E1) =P(E2)-P(E1∩E2)=(0.3-0.1)=0.2. (iv) P(neither E1 nor E2)=P( not E1 and not E2) =P( ¯ E1 and ¯ E2 )=P( ¯ E1 ∩ ¯ E2 ) =P( ¯ E1∪E2 )=1-P(E1∪E2) =1-P(E1∪E2) =(1-0.7)=0.3 [using (i) ].