balls are tossed at random into 50 boxes. Find the expected no of boxes required to get the first ball in the fourth box
Answers
Step-by-step explanation:
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Therefore the probability of getting the ball in the 4th box in the first attempt is 0.0625.
Given:
There are 50 boxes in which the balls are to be tossed.
To Find:
The expected probability of getting the first ball in the fourth box.
Solution:
The given question can be solved by the below-shown approach.
The total number of boxes is 50 which are numbered from 1 to 50.
The ball is thrown into each box starting from 1 to 50 but the ball does not fall into the first 3 boxes and it falls in the 4th box.
So after 3 attempts, we have a total of 47 boxes.
So in the first 3 boxes, the ball may fall or may not fall. Hence both the cases have an equal probability that is 0.5.
Probability of falling in the box = 0.5
Probability of not falling in the box = 0.5
The probability of the ball not falling in the first 3 boxes = 0.5³
The probability of the ball falling in the fourth box after not falling in the first 3 boxes = 0.5³ × 0.5 = 0.5⁴ = 0.0625
Therefore the probability of getting the ball in the 4th box in the first attempt is 0.0625.
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