One of the reasons why the concept of an unfair coin is important in probability is that many real-life experiments can be modeled by a toss of an unfair coin. For example, if the probability of Laverne getting a hit when at bat is 0.36, then batting can be modeled by a toss of an unfair coin for which Heads is associated with Hitting and Tails with Missing. Thus, the probability of Laverne getting 3 hits out of 6 batting attempts is exactly the same as the probability of getting 3 heads from tossing the coin 6 times an can be computed using the following formula P(kH/n) = Cp*(1-p)"-k with n=6, k = 3, and p = 0.36: P(3H/6)=C-0.36³-0.64³20-0.046656 -0.262144= 0.2446 Find the probability of Laverne getting 2 hits out of 9 batting attempts: (Round the answer to 4 decimal places.)

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One of the reasons why the concept of an unfair coin is important in probability is that many real-life
experiments can be modeled by a toss of an unfair coin. For example, if the probability of Laverne getting
a hit when at bat is 0.36, then batting can be modeled by a toss of an unfair coin for which Heads is
associated with Hitting and Tails with Missing. Thus, the probability of Laverne getting 3 hits out of 6
batting attempts is exactly the same as the probability of getting 3 heads from tossing the coin 6 times and
can be computed using the following formula
P(kH/n) = Cp*(1-p)"-k
with n=6, k = 3, and p = 0.36:
P(3H/6)=C-0.36³-0.64³20-0.046656 -0.262144 = 0.2446
Find the probability of Laverne getting 2 hits out of 9 batting attempts:
(Round the answer to 4 decimal places.)
Transcribed Image Text:One of the reasons why the concept of an unfair coin is important in probability is that many real-life experiments can be modeled by a toss of an unfair coin. For example, if the probability of Laverne getting a hit when at bat is 0.36, then batting can be modeled by a toss of an unfair coin for which Heads is associated with Hitting and Tails with Missing. Thus, the probability of Laverne getting 3 hits out of 6 batting attempts is exactly the same as the probability of getting 3 heads from tossing the coin 6 times and can be computed using the following formula P(kH/n) = Cp*(1-p)"-k with n=6, k = 3, and p = 0.36: P(3H/6)=C-0.36³-0.64³20-0.046656 -0.262144 = 0.2446 Find the probability of Laverne getting 2 hits out of 9 batting attempts: (Round the answer to 4 decimal places.)
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given data P(x=k) = nCkpkqn-k _______binomial distributionn = 9P(getting hit) = p = 0.36k = no. of hits laverne getsP(k=2) = ?

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