One box contains six red balls and four green balls, and a second box contains seven red balls and three green balls. A ball is randomly chosen from the first box and placed in the second box. Then a ball is randomly selected from the sec- ond box and placed in the first box. a. What is the probability that a red ball is selected from the first box and a red ball is selected from the second box?
b. At the conclusion of the selection process, what is the probability that the numbers of red and green balls in the first box are identical to the numbers at the beginning?
The probability of choosing two red balls and of identical balls in the first box are given by 0.436 and 0.581 respectively.What is probability?
Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
The zero value of probability indicates that the event will not happen while its value equal to one indicate that it will happen.
(a) As per the question, the probability of choosing red ball from the first box is given as below,
P(Red ball first box) = Number of red balls/ Total balls
⇒ 6/10 = 0.6
Then, after putting the same ball in the second box it can be written as,
P(Red ball second box) = Number of red balls/ Total balls
⇒ 8/11 = 0.727
Thus, the probability of choosing red ball from both the boxes is given as,
P( Both Red balls) = 0.6 × 0.727 = 0.436
(b) The number of balls in the first box will be the same when both the selected balls are either red or green.
Then, it can be written as,
P(Identical balls in first box) = P(Both red balls) + P(Both green balls)
P(Both green balls) = 4/10 × 4/11 = 0.145
Thus, the required probability can be found as below,
P(Identical balls in first box) = 0.436 + 0.145 = 0.581
Hence, the required probabilities for both the cases are 0.436 and 0.581 respectively.
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