Binomial distribution probability: 800 families with 4 kids each; How many families would be expected to have 1) at least 1 boy 2) at most two girls,

[bl363]

Out of 800 families with 4 kids each , how many families would be expected to have 1) at least 1 boy 2) at most two girls 4) children of both sexes . Now in this question first part the soln has a step 1-P(x=0). What is the meaning of this step?

 

[BigBeachBanana]

Out of 800 families with 4 kids each , how many families would be expected to have 1) at least 1 boy 2) at most two girls 4) children of both sexes . Now in this question first part the soln has a step 1-P(x=0). What is the meaning of this step?

At least one boy means one or more. It is more computationally expensive to compute [imath]P(X=1) + ....+P(X=n)[/imath].

It is much easier to use the rule of complement,
[math]P(X=0) + P(X=1) + ....+P(X=n) = 1 \\ P(X=1) + ....P(X=n) = 1-P(X=0)[/math]