Question

10. Suppose that we draw cards repeatedly and with replacement from a file of 100 cards, 50 of which refer to male and 50 to female persons. What is the probability of obtaining the second "female" card before the third "male" card?

Answer 1

Answer:

11/16

Step-by-step explanation:

there are 100 cards out of which there are 50 male and 50 female cards

M= male card F= female cards

P(M)= 50/100= 1/2

P(F)= 50/100= 1/2

Following are the combination in which we can obtain second Female card before Third Male card

FF, FMF, MFF,  MMFF, MFMF, FMMF

So, P(FF)= $\frac{1}{2}\times\frac{1}{2}$= 1/4

P(FMF)=  $\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}$= 1/8

and P(MFF)= $\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}$= 1/8

P(MMFF)= $\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}$

=1/16

P(MFMF)= $\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}$

=1/16

P(FMMF)= $\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}$

=1/16

so the required probability is the sum of all these

=1/4 + 1/8 + 1/8 + 1/16 + 1/16 + 1/16= 11/16