GATE DA 2025 Set 1 — Question 61
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Probability & Statistics → Discrete Random Variables → Binomial
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Question
A bag contains 5 white balls and 10 black balls. In a random experiment, balls are drawn from the bag one at a time with replacement. Let denote the total number of black balls drawn in the experiment.The expectation of denoted by __________
(Round off to one decimal place)
(Round off to one decimal place)
Correct answer
66.6 to 66.7
Solution
Let be an indicator random variable for the -th draw, where if the ball is black and if the ball is white.The probability of drawing a black ball in a single draw is:Since the balls are drawn with replacement, the draws are independent Bernoulli trials. The total number of black balls follows a Binomial distribution .The expectation of a Binomial random variable is given by .Given :Rounding to one decimal place, we get .
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