Question

The Manchester United football club has ‘x’ % chance of losing a game. In a series of ‘n’ matches, find the following probabilities assuming that the distribution of losing a match follows a Binomial distribution. (Use the Dataset H to find the value of’ x’ and’ n’ )  

x		n
1	40		8

         

a. They will win at least’ n-1’ matches.

b. They will lose exactly ‘ n-2 ‘matches.

Answer 1

Sample size , n =    8
Probability of an event of interest, p =   0.4

a)

n-1 = 8-1 =7

Sample size , n =    8
Probability of an event of interest, p =   0.6

	X	P(X)
P ( X = 7) = C (8,7) * 0.6^7 * ( 1 - 0.6)^1=	7	0.0896
P ( X = 8) = C (8,8) * 0.6^8 * ( 1 - 0.6)^0=	8	0.0168

P(at least 7 match) = P(7) + P(8)

=0.1064

b)

n-2= 8-2 =6

Sample size , n =    8
Probability of an event of interest, p =   0.4

	X	P(X)
P ( X = 6) = C (8,6) * 0.4^6 * ( 1 - 0.4)^2=	6	0.0413

=0.0413

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answered by: anonymous