A fair die with six faces is rolled 12 times. What is the probability that an even number (2, 4 or 6) will occur 4 times or more Solution the probability that an even number (2, 4 or 6) will occur 4 times or more = probability of coming 4 times + prob. of coming 5 times ----- + prob. of coming 12 times = (3/6)^4 + (3/6)^5 + (3/6)^6 + (3/6)^7 + (3/6)^8 + (3/6)^9 + (3/6)^10 + (3/6)^11 + (3/6)^12 = 0.124.

1. A fair die with six faces is rolled 12 times. What is the probability that an even number (2, 4 or
6) will occur 4 times or more
Solution
the probability that an even number (2, 4 or 6) will occur 4 times or more =
probability of coming 4 times + prob. of coming 5 times ----- + prob. of coming 12 times =
(3/6)^4 + (3/6)^5 + (3/6)^6 + (3/6)^7 + (3/6)^8 + (3/6)^9 + (3/6)^10 + (3/6)^11 + (3/6)^12 =
0.124