Solution Found!
Suppose that a biased coin that lands on heads with
Chapter 4, Problem 50P(choose chapter or problem)
Problem 50P
Suppose that a biased coin that lands on heads with probability p is flipped 10 times. Given that a total of 6 heads results, find the conditional probability that the first 3 outcomes are
(a) h, t, t (meaning that the first flip results in heads, the second in tails, and the third in tails);
(b) t, h, t.
Questions & Answers
QUESTION:
Problem 50P
Suppose that a biased coin that lands on heads with probability p is flipped 10 times. Given that a total of 6 heads results, find the conditional probability that the first 3 outcomes are
(a) h, t, t (meaning that the first flip results in heads, the second in tails, and the third in tails);
(b) t, h, t.
ANSWER:
Solution
Step 1 of 2
a) We have to find the conditional probability of first 3 outcomes are h,t,t given that a total of 6 heads
Here the first 3 outcomes are h,t,t
From the remaining 7 trials we have to get 5 heads to make a total of 6 heads
Now the probability of getting 5 heads in 7 trials =
Probability of getting 6 heads from 10 trials =
Now
=
=
=
=
=21/210
=1/10
=0.1
Hence the conditional probability of first 3 outcomes are h,t,t given that a total of 6 heads is 0.1