TdIc ogize tie braid name were only 0.50? Additional Exercises 28. When dropped

Question

TdIc ogize tie braid name were only 0.50? Additional Exercises 28. When dropped on a hard surface a thumbtack lands with its sharp point touching the surface with probability 2/3:it lands with its sharp point directed up into the air with probability 1/3. The tack is dropped and its landing position observed 15 times. a. Find the probability that it lands with its point in the air at least 7 times b. If the experiment of dropping the tack 15 times is done repeatedly, what is the average number of times it lands with its point in the air?

Explanation / Answer

Question 28

Solution:

Part a

We are given n = 15, p = 1/3

We have to find P(X7)

P(X7) = 1 – P(X<7) = 1 – P(X6)

P(X6) = 0.796962 (by using binomial table or excel)

P(X7) =1 – P(X6)

P(X7) =1 – 0.796962

P(X7) = 0.203038

Required probability = 0.203038

Part b

Here, we are given n = 15, p = 1/3 = 0.333333

Average = mean = n*p = 15*0.333333 = 4.999995

Average number of times = 5 approximately.

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