Answer: The required value of P(J) is 0.3.
Step-by-step explanation: Given that J and K are independent events and P(J | K) = 0.3.
We are to find the value of P(J).
We know that if A and B are two independent events, then
[tex]P(A\cap B)=P(A)P(B).[/tex]
The conditional probability of event J given that K has already been occured is
[tex]P(J|K)=\dfrac{P(J\cap K)}{P(K)}.[/tex]
Since J and K are independent events, we get
[tex]P(J|K)\\\\\\=\dfrac{P(J\cap K)}{P(K)}\\\\\\=\dfrac{P(J)P(K)}{P(K)}\\\\=P(J).[/tex]
Therefore, we get
[tex]P(J)=P(J|K)=0.3.[/tex]
Thus, the required value of P(J) is 0.3.
