2 A lawyer estimates that 40 of the cases in which she repre

2. A lawyer estimates that 40% of the cases in which she represented the defendant were won. If the lawyer is presently representing ten defendants in different cases, what is the probability that at least five of the cases will be won? What are you assuming here? Hint: binomial distribution

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X < 5) = P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= ( 10 4 ) * 0.4^4 * ( 1- 0.4 ) ^6 + ( 10 3 ) * 0.4^3 * ( 1- 0.4 ) ^7 + ( 10 2 ) * 0.4^2 * ( 1- 0.4 ) ^8 + ( 10 1 ) * 0.4^1 * ( 1- 0.4 ) ^9 + ( 10 0 ) * 0.4^0 * ( 1- 0.4 ) ^10   
= 0.6331
P( X > = 5 ) = 1 - P( X < 5) = 0.3669