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Example Assume that the probability of a bomb dropped from an aeroplane, striking a target is 1/5. If 6 bombs are dropped, find the probability that
(1) exactly two will strike.
(2) at least two strikes the target.

Solution :

Example The probability of a man hitting a target is 1/3. How many must he fire so that the probability of hitting the target, at least once, is more than 90% ?

Solution : Here p = 1/3 and q = 2/3 and n = ?

Now, p (hitting the target at least once) > 90%

p ( x ³ 1) = 1 - p (x = 0) must be greater than 90%

Therefore, he must fire at least 6 times so that the probability of hitting the target at least once is more than 90%

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Example If an average 8 ships out of 10 trials arrive safely at a port. Find the mean and standard deviation of the number of ships arriving safely out of the total of 1600 ships.

Solution : p = 0.8 therefore q = 1 - p = 1- 0.8 = 0.2 and n = 1600

Mean (m) = n p = 1600 ´ 0.8 = 1280

Hence the mean and standard deviation of ships, returning safely respectively 1280 and 16.

Example 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 ?

Solution : n = 10, q = probability that he will clear each hurdle = 5/6

p = probability that he will knock down = 1 - 5/6 = 1/6

Therefore, p (knocking down fewer than 2 hurdles) = p (0) + p (1)

Index

7. 1 Introduction
7. 2 Trial
7. 3 Sample Space
7. 4 Definition of Probability
7. 5 The Laws of Probability
7. 6 Conditional Probability
7. 7 Theoretical Distribution
7. 8 Binomial Distribution
7. 9 Normal Distribution
Chapter 8