my bad for posting 3 questions on 1 post, but I am confused and need help
1. An unfair coin shows heads 2/3 of the time. What is the probability that it shows heads exactly five out of seven flips? Answer should be a common fraction.
Hello Jenny :))
So we need to calculate the probability it shows heads 5 and 2 tails.
That's just 7!/5!/2! = 21.
So there are 21 ways of ordering it.
Now the probability that one of these sequence happens is (2/3)^5*(1/3)^2.
So our answer is (21)*(2/3)^5*(1/3)^2
I hope this helped. :)))