Question

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 Tatiana getting a hit when at bat is 0.29, 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 Tatiana getting 2 hits out of 6 batting attempts is exactly the same as the probability of getting 2 heads from tossing the coin 6 times and can be computed using the following formula with $n = 6$, $k = 2$, and $p = 0.29$: $P(kH/n) = C^n_k p^k (1 - p)^{n-k}$ $P(2H/6) = C^6_2 \cdot 0.29^2 \cdot 0.71^4 = 15 \cdot 0.0841 \cdot 0.254117 = 0.3206$ Find the probability of Tatiana getting 6 hits out of 9 batting attempts: (Round the answer to 4 decimal places.)

          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 Tatiana getting a hit when at bat is 0.29, 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 Tatiana getting 2 hits out of 6 batting attempts is exactly the same as the probability of getting 2 heads from tossing the coin 6 times and can be computed using the following formula
with $n = 6$, $k = 2$, and $p = 0.29$:
$P(kH/n) = C^n_k p^k (1 - p)^{n-k}$
$P(2H/6) = C^6_2 \cdot 0.29^2 \cdot 0.71^4 = 15 \cdot 0.0841 \cdot 0.254117 = 0.3206$
Find the probability of Tatiana getting 6 hits out of 9 batting attempts:
(Round the answer to 4 decimal places.)

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 Tatiana getting a hit when at bat is 0.29, 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 Tatiana getting 2 hits out of 6 batting attempts is exactly the same as the probability of getting 2 heads from tossing the coin 6 times and can be computed using the following formula
with n = 6, k = 2, and p = 0.29:
P(kH/n) = C^nk p^k (1 - p)^n-k
P(2H/6) = C^62 · 0.29^2 · 0.71^4 = 15 · 0.0841 · 0.254117 = 0.3206
Find the probability of Tatiana getting 6 hits out of 9 batting attempts:
(Round the answer to 4 decimal places.)

Added by Charles H.

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