A committee of two persons is selected from 2 men and 2 women.What is the probabality that the committee will have 1) at least one man 2)at most one man

What is the difference betwnn these 2 and also i need solotion for both

the number of men =2 the number of woman = 2.
(i) at least one man : at least one man means either committee has one man or it has two man.
the probability of at least one man = 1- probability of no man
i.e. we will calculate the probability that committee has no man and will subtract it from 1 
=1-C22C24 
=1-16=56
(ii) at most one men = either committee has one man or no man.
case I : committee has one man = C12*C12C24=2*26=23
case II: committee has no man = C22C24=16
thus the probability that committee has at most one man 
=23+16=4+16=56

hope this helps you
 

  • 6

1)

2 C 1 x 2 C 1

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