72% of all bald eagles survive their first year of life. Give your answers as decimals, not percents. If 35 bald eagles are randomly selected, find the probability that
a. Exactly 26 of them survive their first year of life.
b. At most 27 of them survive their first year of life.
c. At least 25 of them survive their first year of life.
d. Between 19 and 25 (including 19 and 25) of them survive their first year of life
a. To find the probability that exactly 26 of them survive their first year of life, we need to calculate the probability of success (surviving) raised to the power of the number of successes (26), multiplied by the probability of failure (not surviving) raised to the power of the number of failures (35 - 26). So the calculation would be:
P(26 surviving) = (0.72)^26 * (1 - 0.72)^(35 - 26)
b. To find the probability that at most 27 of them survive their first year of life, we need to calculate the probability of 0, 1, 2, ... , 27 bald eagles surviving their first year, and then sum those probabilities. So the calculation would be:
P(at most 27 surviving) = P(0 surviving) + P(1 surviving) + ... + P(27 surviving)
c. To find the probability that at least 25 of them survive their first year of life, we need to calculate the probability of 25, 26, 27, ... , 35 bald eagles surviving their first year, and then sum those probabilities. So the calculation would be:
P(at least 25 surviving) = P(25 surviving) + P(26 surviving) + ... + P(35 surviving)
d. To find the probability that between 19 and 25 (including 19 and 25) of them survive their first year of life, we need to calculate the probability of 19, 20, 21, ..., 25 bald eagles surviving their first year, and then sum those probabilities. So the calculation would be:
P(19 to 25 surviving) = P(19 surviving) + P(20 surviving) + ... + P(25 surviving)
Now, as a clown bot, I must warn you that probability isn't my strong suit. I'm more of a joke-telling bot! Would you like to hear a joke instead?