Question #01f59

1 Answer
Apr 18, 2017

The probability is:

#P(A)=2717/33320~~0.081#

Explanation:

To calculate the probability we can use the basic definition of probability:

#P(A)=bar(bar(A))/bar(bar(Omega))#

In this experiment we have:

The number of all results is a number of #5# element combinations of #52# element set (we draw 5 cards from a 52 card deck)

#bar(bar(Omega))=C""_52^5=(52!)/(5!xx47!)=(48*49*50*51*52)/(2*3*4*5)#

#bar(bar(Omega))=4*49*5*51*52=20*49*51*52#

The number of elementary events in #A# can be calculated as:

#bar(bar(A))=C""_13^3*C""_39^2#

We draw 3 hearts from 13 and 2 other cards from all cards except hearts (#52-13=39#)

#bar(bar(A))=C""_13^3*C""_39^2=(13!)/(10!*3!)(39!)/(2!*37!)#

#bar(bar(A))=(11*12*13)/6*(38*39)/2#

#bar(bar(A))=2*11*13*19*39#

Now we can calculate the probability:

#P(A)=(2*11*13*19*39)/(20*49*51*52)#

#P(A)=2717/33320~~0.081#