Binomial Probabilities

#1
Please help me with these two math problems!

Please help me with these statistics problems! I'm really new to this online program for school and it's really hard without a teacher or peers to ask for help! :(

Approximately 2% of the nation's children (about 1.7 million) have a parent who is in jail or prison. Let X be the number of children that have an incarcerated parent from a random sample of 100 children.
a) Verify that this is a binomial setting and write it in notation.
b) Describe what P(X = 0) means in context.
c) Find P(X = 0) and P(X = 1).
d) What is the probability that two or more of the children have a parent in jail or prison?


Dilbert forgot to study for the multiple-choice exam. Each question has four choices and there are 50 questions. Dilbert, in his infinite wisdom, decides to randomly guess on each problem. Find the probability for each:
a) If Dilbert gets 30 or more right, he will be named the company CEO.
b) If Dilbert gets 20 to 29 right, he will be promoted and get a 10% raise.
c) If Dilbert gets 10 to 19 right, he will get to keep his menial job and pay.
d) If Dilbert gets less than 10 right, he will be kicked out of cubicle central and unemployed.
 
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