What is the probability of tossing 21 or more heads or more out of 30 tosses? Answer to 2 decimal places as a percent.Ex: if your answer is 4.545% answer 4.55 Use Stapplet. square

To find the probability of getting 21 or more heads out of 30 tosses, we can use the binomial probability formula. The binomial probability formula is given by:<br /><br />$P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$<br /><br />where:<br />- $n$ is the number of trials (in this case, 30 tosses)<br />- $k$ is the number of successes (in this case, 21 or more heads)<br />- $p$ is the probability of success on a single trial (in this case, 0.5 for a fair coin)<br /><br />We need to calculate the probability of getting 21, 22, 23,..., up to 30 heads. This can be done by summing the individual probabilities for each value of $k$ from 21 to 30.<br /><br />$P(X \geq 21) = P(X = 21) + P(X = 22) + P(X = 23) + \ldots + P(X = 30)$<br /><br />Using the binomial probability formula, we can calculate each term individually and then sum them up.<br /><br />$P(X = 21) = \binom{30}{21} (0.5)^{21} (0.5)^{9}$<br />$P(X = 22) = \binom{30}{22} (0.5)^{22} (0.5)^{8}$<br />$P(X = 23) = \binom{30}{23} (0.5)^{23} (0.5)^{7}$<br />$\vdots$<br />$P(X = 30) = \binom{30}{30} (0.5)^{30} (0.5)^{0}$<br /><br />Now, we can calculate each term using the binomial coefficient and plug in the values of $n$, $k$, and $p$.<br /><br />$P(X = 21) = \frac{30!}{21! \cdot 9!} \cdot (0.5)^{21} \cdot (0.5)^{9}$<br />$P(X = 22) = \frac{30!}{22! \cdot 8!} \cdot (0.5)^{22} \cdot (0.5)^{8}$<br />$P(X = 23) = \frac{30!}{23! \cdot 7!} \cdot (0.5)^{23} \cdot (0.5)^{7}$<br />$\vdots$<br />$P(X = 30) = \frac{30!}{30! \cdot 0!} \cdot (0.5)^{30} \cdot (0.5)^{0}$<br /><br />After calculating each term, we can sum them up to get the final probability.<br /><br />$P(X \geq 21) = P(X = 21) + P(X = 22) + P(X = 23) + \ldots + P(X = 30)$<br /><br />Finally, we can convert the probability to a percentage by multiplying it by 100.<br /><br />$P(X \geq 21) \times 100\%$<br /><br />The final answer will be the probability of getting 21 or more heads out of 30 tosses, expressed as a percentage.