Question -
| P(A) | P(B) | P(A ∩ B) | P(A ∪ B) |
| (i) | 1/3 | 1/5 | 1/15 | …. |
| (ii) | 0.35 | ….. | 0.25 | 0.6 |
| (iii) | 0.5 | 0.35 | …. | 0.7 |
Answer -
From the given table,
(i) P(A) = 1/3, P(B) = 1/5, P(A ∩ B) = 1/15, P(A ∪ B) = ?
We know that,
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
= (1/3) + (1/5) – (1/15)
= ((5 + 3)/15) – (1/15)
= (8/15) – (1/15)
= (8 – 1)/15
= 7/15
(ii) P(A) = 0.35, P(B) = ?, P(A ∩ B) = 0.25, P(A ∪ B) = 0.6
Then,
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
0.6 = 0.35 + P(B) – 0.25
Transposing – 0.25, 0.35 to LHS and it becomes 0.25and –0.35.
P(B) = 0.6 + 0.25 – 0.35
= 0.5
(iii) P(A) = 0.5, P(B) = 0.35, P(A ∪ B) = 0.7, P(A ∩ B) = ?
Then,
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
0.7 = 0.5 + 0.35 – P(A ∩ B)
Transposing – P(A ∩ B) to LHS and it becomes P(A ∩ B) and0.7 to RHS and it becomes – 0.7.
P(A ∩ B) = 0.85 – 0.7
= 0.15