Rework problem 9 from section 3.2 of your text, involving independent and disjoint events. For this problem, assume that Pr[A∪B]=0.7 and Pr[A]=0.25.

Two events are said to be Disjoint or Mutually Exclusive if the two events can not happen at the same time. For example when we throw a die getting an even number is disjoint to getting an odd number.

I. e Probability (A∩B) = 0

Let me explain this concept through venn diagram.

Pr[A∪B]=0.7, Pr[A]=0.25

Since events are Disjoint

Pr[A∩B]=0

Pr[A∪B]=Pr[A] + Pr[B]

0.7=0.25 + Pr[B]

0.7-0.25=Pr[B]

⇒Pr[B]=0.45=45/100=9/20

Now events are said to be independent if Pr[A and B]=Pr[A] * Pr[B]

Events are said to be independent if occurrence of one is not affected by occurrence of other. For example getting multiple of 2 as one event and getting multiple of 3 as second event when we throw a die.

Pr[A∪B]=0.7, Pr[A]=0.25

Pr[A∪B] = Pr[A] + Pr[B]-Pr[A∩B]

But Pr[A∩B] = Pr[A] * Pr[B]

⇒Pr[A∪B] = Pr[A] + Pr[B] - Pr[A] * Pr[B]

⇒0.7=0.25+p-0.25*p

⇒0.7-0.25=p - 0.25 p

⇒0.45=0.75 p

⇒p = 0.45/0.75

⇒p = 3/5