PLEASE HELP ON THIS ASAP I HAVE A TEST ON IT

Question

In the United States the probability that a person has chapped lips is 30% On Charlene's next five dates. What is the probability that: at least four of the dates have chapped lips?

show work please

Answer 1

If the events are independent, then the combined probability is the product of the individual probabilities.

When you say "at least", the logic is different. Consider 3 coins. there are 8 possible outcomes. If you want to known the odds of getting at least 2 heads, that is the sum of the odds of getting 2 heads and the odds of getting 3:

Odds of 2 heads: 1/2 * 1/2 = 1/4

Odds of 3 heads: 1/8

Odds of at least 2 heads 1/4 + 1/8 = 3/8

Consider the opposite case: the odds of getting LESS THAN heads--i.e. either one or none. This is the "opposite" event and therefore the probability has to be 1 = 3/8 = 5/8.

Prove it by noting the probability of NO heads: 1/8 and the probability of ONE head: 1/2.

1/2 + 1/8 = 5/8