# Let E1

Given that P(E1) =P1 and P(E2) =P2

(i)P1P2

=P(E1). P(E2) =P (E1 Ո E2)

So, E1 and E2 occur simultaneously.

(ii)(1-P1) P2

As we know P(A)+P(A) = 1

=P(E1)’. P(E2)

= P (E1’ Ո E2)

So, E1 does not occur but E2 occur.

(iii)1-(1-P1) (1-P2)

As we know P(A)+P(A) = 1

=1-P(E1)’P(E2)’

=1-P (E1’ Ո E2’)

By De Morgan’s laws: =1-P (E1 Ս E2)

As we know P(A)+P(A) = 1

= 1- [1-P (E1 Ս E2)]

= P (E1 Ս E2)

So, either E1 or E2 or both E1 and E2 occurs.

(iv)P1+P2-2P1P2

= P(E1) + P(E2) – 2P(E1) P(E2)

= P(E1) + P(E2) – 2P (E1 Ո E2)

= P (E1 Ս E2)- 2P (E1 Ո E2)

So, either E1 or E2 occurs but not both.

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