जॉइन Examsbookउत्तर : 2. "19/42"
A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.5
प्र: A bag contains 4 red and 3 black balls. A second bag contains 2 red and 4 black balls. One bag is selected at random. From the selected bag, one ball is drawn. Find the probability that the ball drawn is red.
- 123/42false
- 219/42true
- 37/32false
- 416/39false
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उत्तर : 2. "19/42"
व्याख्या :
Answer: B) 19/42 Explanation: A red ball can be drawn in two mutually exclusive ways (i) Selecting bag I and then drawing a red ball from it. (ii) Selecting bag II and then drawing a red ball from it. Let E1, E2 and A denote the events defined as follows: E1 = selecting bag I, E2 = selecting bag II A = drawing a red ball Since one of the two bags is selected randomly, therefore P(E1) = 1/2 and P(E2) = 1/2 Now, PAE1 = Probability of drawing a red ball when the first bag has been selected = 4/7 PAE2 = Probability of drawing a red ball when the second bag has been selected = 2/6 Using the law of total probability, we have P(red ball) = P(A) = PE1×PAE1+PE2×PAE2 = 12×47+12×26=1942