A kindergarten class has four left-handed children and fourteen right-handed chi

Question

A kindergarten class has four left-handed children and fourteen right-handed children. Two children are selected without replacement for a shoe-tying lesson. Let X = the number who are left-handed. a) The simple events in the sample space are {RR, RL, LR, LL}. For instance, one simple event is RL, indicating that the first child is right-handed and the second one is left-handed. Find the probability for each of the simple events in the sample space. P(RR) = P(RL) = P(LR) = P(LL) (b) Find the probability distribution function for X.

Explanation / Answer

a) as all four events are equally likely therefore probability for each of the simple events in the sample space =1/4

hence P(RR) = P(RL) = P(LR) = P(LL) =1/4

b)

for P(X=0) =P(no left handed person) =P(RR )=1/4

P(X=1) =P(one left handed person) =P(LR)+P(RL) =1/4+1/4 =1/2

P(X=2) =P(both left hand)=P(LL) =1/4

hence probability distirbution of X:

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