A nationwide survey showed that 65% of all children in the United States dislike eating vegetables. If 4 children are chosen at random, what is the probability that all 4 dislike eating vegetables? (Round your answer to the nearest percent.)

The answer is 18% but how and why?

To find the probability that all 4 children chosen at random dislike eating vegetables, we need to calculate the probability of one child disliking vegetables and then multiply it by itself four times, since there are four children.

Given that the nationwide survey showed that 65% of all children dislike eating vegetables, the probability of one child disliking vegetables is 65% or 0.65.

So, the probability that all 4 children dislike eating vegetables can be calculated as follows:

P(all 4 dislike vegetables) = P(first child dislikes) * P(second child dislikes) * P(third child dislikes) * P(fourth child dislikes)

P(all 4 dislike vegetables) = 0.65 * 0.65 * 0.65 * 0.65

P(all 4 dislike vegetables) ≈ 0.179

To round the answer to the nearest percent, we multiply by 100 and round to the nearest whole number:

P(all 4 dislike vegetables) ≈ 0.179 * 100 ≈ 18%

Therefore, the probability that all 4 children chosen at random dislike eating vegetables is approximately 18%.

To find the probability that all 4 children dislike eating vegetables, we need to multiply the probabilities of each child disliking vegetables.

Given that the nationwide survey showed that 65% of all children in the United States dislike eating vegetables, it means that the probability of any child disliking vegetables is 0.65 or 65%.

To find the probability that all 4 children dislike eating vegetables, we multiply this probability four times since we want all 4 children to dislike vegetables.

0.65 * 0.65 * 0.65 * 0.65 = 0.179

Multiplying these probabilities gives us 0.179.

Finally, we round the answer to the nearest percent, giving us 18%.

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

.65^4 = ?