A Die is Biased so that the probability of throwing a 5 is 0.75 and the probabilities of throwing a 1,2,3,4 or 6 are all equal.
i. The Die is thrown three times. Find the probability that the result is a 1 followed by a 5 followed by any even number.
My Attempt: P of 5: 0.75 for 1,2,3,4,6: 0.05
So P( 1 followed by 5 and then even)= 0.05 x .075 x (0.05+0.05+0.05) (adding because of "or")
= 0.0005625
ii. Find the Probability that, out of 10 throws of this die, at least 8 result in a 5.
My attempt: using binomial p = .75 q=.25
n=10
p(x ≥ 8) = p(x=8) + p(x=9) + p(x=10)
= 10C8 (.75)^8 (0.25)^2 + 10C9 (0.75)^9 (0.25)+ 10C10 (0.75)^10 (0.25)^0
iii. The die is thrown 90 times. Using an appropriate approximation, find the probability that a 5 is thrown more than 60 times.
Please solve this one. We have studied binomial and normal Distribution Only
Please check my attempts and tell me is it correct? if wrong tell me where did i go wrong. and please give ur advices too. My Exam is on 24th May So need Tips