7 Find the probability of getting exactly 2 heads in 10 tosses of a fair coin.(1

Question

7 Find the probability of getting exactly 2 heads in 10 tosses of a fair coin.(10 8 Find the area under the standard normal curve between-0.4 and z 2.1.(10 9 Starting at a fixed time, we observe the gender of each newborn child at a certain points) points) hospital until a boy (B) is born. Let p P(B), assume that successive births are independent, let X to be the number of births observed. Find the probability mass function of X.(10 points) 10 Find the probability of getting between 3 and 6 heads inclusive in 10 tosses of a fair coin by using (a) the binomial distribution and (b) the normal approximation to the binomial distribution. (10 points)

Explanation / Answer

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7)

let p =probability of getting a head = 1/2 =0.5

q=1-p =1-0.5 =0.5

n=10

We would be using binomial distribution formula here

P=nCr p^r q^(n-r)

r=2

P(exactly 2 heads) = P(x=2) = 10C2 (0.5)^2 (0.5)^(10-2)

                                                 = 45 * 0.25 * 0.5^8

                                                 = 45 * 0.25 * 0.00390625

                                                 = 0.0439

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