A randomized controlled experiment has 50 participants, of whom20 are women. A simple random sample of 25 participants areassigned to the treatment group and the remainder to the controlgroup.
a) Say whether the following statement is trueor false. If it is true, provide a math expression for the chance.If it is false, provide math expressions for the two chances.
?(the treatment group has 16 women) = ?(the control group has 16women)P(the treatment group has 16 women) = P(the control group has16 women)
b) Say whether the following statement is trueor false, and justify your answer.
The event \"the treatment group has 16 women\" is independent ofthe event \"the control group has 16 women\".
c) Write a math expression for the chance thatthere are at least six women in both groups.
[Hint: This can be done by just thinking about the women in oneof the groups. Any other way will prove quite a bit harder.]
