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In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is 5/6. What is the probability that he will knock down fewer than 2 hurdles?
In this question,
Let us assume p be the probability of player that will clear the hurdle while q be the probability of player that will knock down the hurdle
∴
And,
Let us also assume X be the random variable that represents the number of times the player will knock down the hurdle
∴ By binomial distribution,
Hence, probability (players knocking down less than 2 hurdles) = P (X < 2)
= P (X = 0) + P (X = 1)
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Suppose we have four boxes A, B, C and D containing coloured marbles as given below:
Box | Marble colour | ||
Red | White | Black | |
A | 1 | 6 | 3 |
B | 6 | 2 | 2 |
C | 8 | 1 | 1 |
D | 0 | 6 | 4 |
One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C?