Question

If E1 and E2 are independent events such that P (E1) = 0.3 and P (E2) = 0.4, find (i) P (E1 ∩ E2) (ii) P (E1 U E2) (iii) P(bar E1 ∩ bar E2) (iv) P(E1 ∩ E2) Select the correct answer from above options

Answer 1

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