A coin whose probability of heads is 04 is tossed 25 times F

A coin whose probability of heads is 0.4 is tossed 25 times. Find the probability that the number of heads is

(a) less than 13

(b) exactly 11

Let X denote the number of heads. Then X is Binominal (25, 0.4)

P(X)= 25Cx(0.4)^x(0.75^(25-x) x=0,1, ....25

(a) P(less than 13) =P(0)+P(1)+ ...+P(12) =25C0(0.4)^0(0.75^(25-0) + .... + 25C12(0.4)^12(0.75^(25-12)

= 0.8462 use the excel function =BINOMDIST(12,25,0.4,1) to find this value

(b) P(exactly 11)=P(11)= 25C11(0.4)^11(0.75^(25-11)

= 0.1465 USE EXCEL FUNCTION =BINOMDIST(11,25,0.4,0)