A nationwide survey showed that 65 percent of all children in the US dislike eating vegetables If three are chosen at randomwhat is probability vegetables?

To calculate the probability that none of the three children chosen at random dislike eating vegetables, we can use the complement rule. The complement rule states that the probability of an event not happening is equal to 1 minus the probability of the event happening. In this case, the probability that a child does not dislike eating vegetables is 1 - 0.65 = 0.35.

Since we are choosing three children, and we want none of them to dislike eating vegetables, we need to multiply the probability that each child does not dislike eating vegetables by itself three times. Therefore, the probability that none of the three children chosen at random dislike eating vegetables is:

$$ P(none \ dislike \ vegetables) = (0.35)^3 \approx 0.042875 $$

This means that there is approximately a 4.3% chance that none of the three children will dislike eating vegetables.