यदि A प्रतिदर्श समष्टि (sample space) से संबद्ध कोई घटना है, और E1, E2, E3 परस्पर अपवर्जी और निश्शेष घटनाएं हैं। तो निम्नलिखित में से कौन से कथन सत्य हैं? (A) P(A) = P(E1)P(E1 | A) + P(E2)P(E2 | A) + P(E3)P(E3 | A) (B) P(A) = P(A | E1)P(E1) + P(A | E2)P(E2) + P(A | E3)P(E3) (C) P(Ei | A) = P(A | Ei)P(Ei)∑i=13 P(A | Ei)P(Ei), i = 1, 2, 3 (D) P(A | Ei) = P(Ei | A)P(Ei)∑i=13 P(Ei | A)P(Ei), i = 1, 2, 3 नीचे दिए गए विकल्पों में से सही उत्तर का चयन कीजिए:

A box contains 'x + 4' red, 'x – 1' green and 'x – 5' blue balls. If two balls are drawn from the bag one after another without replacement, then the probability of getting one red and one green ball is equal to the probability of getting a sum equal to or more than 8 when two fair dice are rolled. Find the probability of drawing a red ball when one ball is drawn at random from the bag.

Four persons are chosen at random from a group containing 3 men, 2 women, and 4 children. The probability that exactly two of them are children is: