5. For two events A and B, the following probabilities are given Pn-0.33 P-0.45

Question

5. For two events A and B, the following probabilities are given Pn-0.33 P-0.45 Note PA and B) PAMPUR PA)0.52 Use the appropriate laws of probabilities to caleulate A) not() B) P(A and B C) Pld or B) 6. A homework assignment consists of 10 exercises. Your instructor will grade only two exercises selected at random. You have solved correctly 6 exercises. Calculate the probability that A) Both exercises are incorrect B) One exercise is incorrect and the other is correct 7. The probability distribution of X is given by the function (x)2 for x-3,4,5,6,7... 40 Find P[X-3] 8. Calculate the mean of the distribution of X 0.4 0.1 0.2 0.1 0.2 Total

Explanation / Answer

5 )

P( A ) = 0.52 , P( B ) = 0.33 , P( A | B ) = 0.45

A ) Not B .

P( not B ) = 1 - P(B) = 1 - 0.33 = 0.67

B) P( A and B )

P( A and B ) = P( A | B )*P(B) = 0.45*0.33 = 0.1485

c) P( A or B)

P( A or B) = P( A) + P( B ) - P( A and B ) = 0.52 + 0.33 - 0.1485 = 0.7015

6)

Out of 10 excercises 6 are correct and 4 are incorrect.

a)

Total number of ways to select 2 exercises out of 10 = 10C2 = 45

Number of ways to select 2 incorrect exercises out of 4 = 4C2 = 6

So, P( Both exercises are incorrect ) = 6 / 45 = 0.1333

b)

Number of ways to select one incorrect and one correct exercises = 6C1 x 4C1 = 24

Total number of ways to select 2 exercises out of 10 = 10C2 = 45

So, P( One exercises is incorrect and other is correct ) = 24/45 = 0.5333

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