It is given that E1 and E2 are independent events such that P (E1) = 0.3 and P (E2) = 0.4
(i) P (E1 ∩ E2)
We know that E1 and E2 are independent events
P (E1 ∩ E2) = P (E1) × P (E2)
By substituting the values
= 0.3 × 0.4
= 0.12
Hence, P (E1 ∩ E2) = 0.12 when E1 and E2 are independent events.
(ii) P (E1 U E2) when E1 and E2 are independent events
P (E1 U E2) = P (E1) + P (E2) – P (E1 ∩ E2)
By substituting the values
= 0.3 + 0.4 – 0.12
= 0.58
Hence, P (E1 U E2) = 0.58 when E1 and E2 are independent events.
(iii)
It is given that E1 and E2 are independent events so even
bar E1 and bar E2 are also independent