Grade 12U Mathematics Problem?
I'm having a bit of trouble figuring out how to solve some math problems. It's Grade 12U Mathematics of >Update:
3) A die is rolled 10 times and 6 times it comes up 5.
(a) What is the probability of this occuring?
(b) Conduct a simulation to show that this is an unfair die.
4) A penny is placed in the bottom row of an eight-by-eight grid. If the penny can be moved one square at a time to the row above, either diagonally or straight ahead, how many paths will lead to the square in the top left-hand corner?
Note: the penny is placed on the 3rd grid from the right (bottom row).
Comments
2 looks more interesting. As such, I will do it.
P(double 3s on 1 double roll) = 1/36
P(double 3s are rolled 5 times out of 30) = 30C5*(1/36)^5*(35/36)^25, where 30C5 is the combination operator
b) P(double 3s never rolled) = (35/36)^30
P(double 3s rolled at least once) = 1 - (35/36)^30
1) to get started...
a) P(3 white marbles in 4) = (10C3)*(6C1)/(16C4)