A pair of fair coins is thrown repeatedly until a pair of tails is obtained. The random variable $$\(X\)$$ denotes the number of throws required to obtain a pair of tails. On a different occasion, a pair of fair coins is thrown 80 times. Use an approximation to find the probability that a pair of tails is obtained more than 25 times. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s20_qp_53 Year：2020 Question No：5(d)
Answer:
Mean \(=80 \times 0.25=20\)
Var \(=80 \times 0.25 \times 0.75=15\)
\(\mathrm{P}(\) more than 25\()=\mathrm{P}\left(z>\frac{25.5-20}{\sqrt{15}}\right)\)
\(\mathrm{P}(z>1.42)\)
\(1-0.9222\)
\(0.0778\)
Var \(=80 \times 0.25 \times 0.75=15\)
\(\mathrm{P}(\) more than 25\()=\mathrm{P}\left(z>\frac{25.5-20}{\sqrt{15}}\right)\)
\(\mathrm{P}(z>1.42)\)
\(1-0.9222\)
\(0.0778\)
Knowledge points:
5.5.3 recall conditions under which the normal distribution can be used as an approximation to the binomial distribution, and use this approximation, with a continuity correction, in solving problems. (n sufficiently large to ensure that both np > 5 and nq > 5.)
Solution:
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