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+1 vote
22.9k views
in Probability by (49.9k points)
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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 E∩ bar E2)

(iv) P(E1 ∩ E2)

2 Answers

+2 votes
by (48.6k points)
selected by
 
Best answer

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

+1 vote
by (1.3k points)
(i) 0.12

(ii)0.82

(iii)0.42

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