Question

Question 3. A sports club consists of 32% persons who play badmintonand 60% persons who play tennis. 10% of the sports club members playboth badminton and tennis. What is the --probability that a randomly selected person in the club plays neither tennis nor badminton?

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What is the number of non-negative integer solutions to the equation:

x1+x2+x3= 25

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In answering a question on a multiple choice test, a studenteither knows the answer or the student just guesses. Suppose that theprobability that the student knows the answer is 0.75, and the probabil-ity that he guesses is 0.25. Assume that the probability that the student’sguesses will be correct is 0.20. What is the conditional probability thatthe student guessed the answer to a question given that he answered itcorrectly?

Answer 1

Solution 3:

Probability of a person playing badminton, P(B) = 0.32

Probability of a person playing tennis, P(T) =0.60

Probability of a person playing both tennis and badminton, P(BandT) = 0.10

So, Probability of a person playing either tennis or badminton,

P(BUT) = P(B) + P(T) - P(BandT) = 0.32+0.60-0.10= 0.82

Therefore, Probability of a person playing neither tennis nor badminton = 1 - P(BUT) = 1 - 0.82 = 0.18

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Solution: The number of non negative integral solution of the equation X1 + X2 + .......Xn = r is = (r+n-1)C(n-1)

So for the equation X1 + X2 + X3 = 25 total number of non negative integral solutions are (25+3-1)C(3-1) = (27)C(2) = 351

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Solution:

Probability that student knows the answer, P(K) = 0.75

Probability that student guesses the answer, P(G) = 0.25

Probability of correct when student guesses, P(C/G) = 0.2

Probability of incorrect when student guesses, P(NC/G) = 0.8

Assuming that when the student thinks he knows that answer he always gets it correct. So an answer to a question can be incorrect only if it was guessed.

So Probability of Not correct, P(NC) = P(G)*P(NC/G)

Probability that student guesses given answer is incorrect,

P(G/NC) = (P(NC/G)*P(G))/P(NC)

= 1.