Test tomm. Need help *Urgent*
posted by Tom .
Sorry for posting so many topics, but I really need help on this stuff. I recently lost my work I did on a separate sheet from 2 weeks ago, and now I can't seem to find the answer again.
a fair sixsided die is tossed seven times in a row.
A) What is the probability that a "4" comes up exactly four times? (I got 4375/279936)
B) What is the probability that a "4" comes up an even number of times? (I got 2315/4374)
C) What is the probability that a number higher than "4" Comes up exactly four times (I got 280/2187)
Can anyone help me with this. I need to know how I got these answers again.

Assistance needed.

Tom, I answered part a) in
http://www.jiskha.com/display.cgi?id=1211429814
for b) using the same argument it would be
prob(exactly 2 times) + prob(exactly 4 times) + prob(exactly 6 times)
= C(7,2)(1/6)^2(5/6)^5 + C(7,4)(1/2)^4(5/6)^3 + C(7,6)(1/6)^6(5/6)
= 70035/279936 which is not what you had
but check my calculations. 
B) I believe the middle term in Reiny's formula should be
C(7,4)(1/6)^4(5/6)^3
= C(7,4)*5^3/6^7
= 35*125/279,936 = 4375/279,936
which is the same as the answer to (A)
C(7,2)(1/6)^2(5/6)^5 = 21*3125/279,936
= 65625/279,936
C(7,6)(1/6)^6(5/6) = 7*5/279,936
= 35/279,936
Total = 70035/279936 = 0.25018
I agree with Reiny's final (B) answer, so the (1/2)^4 was probably a typo that should have been (1/6)^4
C) Since is equally likely to get "5" or "6" four times as it is to get "4" four times, just double the answer to (A). That does not agree with your answer.