Question

The accompanying Venn diagram shows three events, A,B and C and also the probabilities of the various intersections (for instance,$p(A\cap B)=.07)$ Determine

(i) $P\left(A\right)$
(ii) $P(B\cap \overline{C})$
(iii) $P(A\cup B)$
(iv) $P(A\cap \overline{B})$
(v) $P(B\cap C)$
(vi) Probability of exactly one of three occurs.

Answer 1

Obtaining the required values observing the Venn diagram P(A) From the Venn diagram.
(i) $P\left(A\right)$

$P\left(A\right)=0.13+0.07=0.20$

Final Answer:$0.20$

(ii) Obtaining the required values observing the Venn diagram
$P(B\cap \overline{C})$
From the Venn diagram.

$P(B\cap \overline{C})=P\left(B\right)-P(B\cap C)$
$=(0.07+0.10+0.15)-0.15$
$=0.07+0.10+0.15-0.15$
$=0.17$
Final Answer : $0.17$

(iii)
Obtaining the required values observing the Venn diagram
$P(A\cup B)$
From the Venn diagram.

$P(A\cup B)=0.13+0.07+0.15+0.10$
$=0.45$
Final answer : $0.45$

(iv) Obtaining the required values observing the Venn diagram
$P(A\cap \overline{B})$
From the Venn diagram.


$P(A\cap \overline{B})=P\left(A\right)-P(A\cap B)$
$=0.13+0.07-0.07$
$=0.13$
Final Answer: $0.13$

(v) Obtaining the required values observing the Venn diagram
$P(B\cap C)$
From the Venn diagram.

$P(B\cap C)=0.15$
Final Answer : $0.15$

(vii) Obtaining the required values observing the Venn diagram
Probability of exactly one of the three occurs.
From the Venn diagram.

P(Exactly one of the three occur)
$=0.13+0.10+0.28$
$=0.51$
Final answer: $0.51$