Question

The Probability that at least one of the events E1 and E2 will occur is 0.6. If the probability of their occurrence simultaneously is 0.2, then find P( ˉ E 1)+P( ˉ E 2) Select the correct answer from above options

Answer 1

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Given, P(E1∪E2)=0.6andP(E1∩E2)=0.2.

∴P(E1∪E2)=P(E1)+P(E2)-P(E1∩E2)

⇒P(E1)+P(E2)=P(E1∪E2)+P(E1∩E2)=(0.6+0.2)=0.8

⇒P(E1)+P(E2)=0.8

⇒{1-P(

¯

E1

)}+{1+P(

¯

E2

)}=0.8

⇒P(

¯

E1

)+P(

¯

E2

)=(2-0.8)=1.2.

Hence, P(

¯

E1

)+P(

¯

E2

)=1.2.