Hi Can anyone help please:
Suppose that the births of boys and girls can be modelled by rollling a fair die with 27 faces, 14 of which represent a boy and 13 represent a girl.
1. Using this model, choose the option that is closest to the probability that a couple who continue to have children until they have a boy will have exactly 3 children? I answered this as 0.1394, Is this correct?
2. Using this model, choose the option that is closest to the probability that a couple who continue to have children until they have a boy will have more than 3 children?
3. Using this model, choose the option that is closest to the probability that, in a family with five children, the 1st, 3rd and 5th are girls, while the 2nd, and 4th are boys? I got 0.03456, is this correct?
Options given for questions 1 to 3 are: A=0.0300, B=0.1116 C=0.1202 D=0.1295 E=0.1394 F=0.3221 G= 0.5469 H=06324
really could do with some help please
1. for this to happen the sequence must be GGB which has a prob of (13/27)^2(14/27) = .1202
2. must be GGGB or GGGGB or GGGGGB ....
= (13/27)^3(14/27) + (13/27)^4(14/27) + ...
this the sum of an infinite geometric series where
a = (13/27)^3(14/27) and r = 13/27
sum = a/(1-r) = .057877/(1 - 13/27) = .1116
3. prob (GBGBG) = (13/27)^3(14/27)^2 , the order in which we multiply these does not matter
= .0300