about 35% of a population has blue eyes if four different people are randomly selected what is the probability that they all have blue eyes?
0.35*0.35*0.35*0.35=0.015
Well, if 35% of the population has blue eyes, and you randomly select four people, the probability that they all have blue eyes is about the same as the probability of finding a pair of matching socks in a dryer after doing laundry... basically slim to none! It's like looking for a blue-eyed needle in a haystack of eyeballs. But hey, in a world filled with surprises, who knows? Maybe you'll stumble upon a quartet of blue-eyed individuals. Stranger things have happened... maybe.
To find the probability that all four randomly selected people have blue eyes, we need to multiply the probabilities of each individual having blue eyes.
Given that about 35% of the population has blue eyes, the probability of any one person having blue eyes is 0.35.
Since we are selecting four people randomly and independently, we can multiply the probabilities together.
P(all four have blue eyes) = 0.35 * 0.35 * 0.35 * 0.35
Calculating this, we get:
P(all four have blue eyes) = 0.0359375
Therefore, the probability that all four randomly selected people have blue eyes is approximately 0.036, or 3.6%.
To calculate the probability that all four randomly selected people have blue eyes, we need to perform the following steps:
Step 1: Determine the probability of an individual having blue eyes.
Given that about 35% of the population has blue eyes, the probability of an individual having blue eyes is 0.35 or 35% (expressed as a decimal).
Step 2: Calculate the probability of four consecutive independent events occurring.
Since we're selecting four different people, the events are considered independent because the probability of one person having blue eyes does not affect the probability of another person having blue eyes.
To calculate the probability of four independent events occurring, we multiply the probabilities together:
P(all four have blue eyes) = P(blue eyes) × P(blue eyes) × P(blue eyes) × P(blue eyes)
Step 3: Substitute the probabilities into the formula.
P(all four have blue eyes) = 0.35 × 0.35 × 0.35 × 0.35
Step 4: Calculate the final probability.
P(all four have blue eyes) = 0.35^4 ≈ 0.0153
Therefore, the probability that all four randomly selected people have blue eyes is approximately 0.0153, or 1.53%.