Can someone please help me with Probability (2) questions

[thancock]

1)In an office football pool, there are 10 closely matched games this week (i.e., either team has a
50-50 chance). A participant in the pool picks each game’s winner at random by using a coin flip.
(a) What is the probability that he picks all 10 games correctly? (b) At least 5 games? (c) Fewer
than 3 games? (d) No more than 6 games?

2)If Punxsutawney Phil sees his shadow on the first Monday in February, then legend says that winter
will last 6 more weeks. In 118 years, Phil has seen his shadow 104 times. (a) What is the probability
that Phil will see his shadow on a randomly chosen Groundhog Day? (b) What kind of
probability is this? (Data are from www.groundhog.org.)


I really appreciate the help

 

[thancock]

I figured out the second one but I still need help with the first one.

 

[tutor_joel]

First of all, you should know that this number should be very small.
This is the multiplication rule. There is a 0.5 chance of 1 event occurring correctly 10 times in a row. So, 0.5^10

"at least" 5 games would be more complicated. There is a formula for this I'll have to look up