Statistics- MATH-105- ASS. 2 Q1) A package of three types of items: 2000 small i

Question

Statistics- MATH-105- ASS. 2 Q1) A package of three types of items: 2000 small items, 1000 medium items and 500 big items. Find a) The probability of small or medium. b) The probability of small or big. c) The probability of big or medium. d) The probability of small and medium. e) The probability of small, medium and big items. Q2) Consider the sets: A={ 1,2,..,9), B={5, 9) AND Cs(1,2) Find the probability of the intersection and the union of A with B ; A with C? What is the probability for each element in A, B and C. Q3) What is the probability of selection 5 students from 11 randomly for a conference? What is the probability of selection the first 4-th students from 11?

Explanation / Answer

1) Total items = 2000 + 1000 + 500 = 3500

a) P(small or medium) = P(small) + P(medium) = 2000/3500 + 1000/3500 = 6/7

b) P(small or big) = P(small) + P(big) = 2000/3500 + 500/3500 = 5/7

c) P(big or medium) = P(big) + P(medium) = 500/3500 + 1000/3500 = 3/7

d) P(small and medium) = 0

e) P(small, medium and big) = 0

2)

a) P(A U B) = 9/9 =1

P(A B) = 5/9

b) P(A U C) = 9/9 =1

P(A C) = 2/9

c) P(A) = 9/9 = 1

P(B) = 5/9

P(C) = 2/9

3) Question is incomplete. It is not given how many students are there to choose and how many needed to choose.

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