The question is to draw two cards from a standard deck without replacement. To win, both cards must be face cards. What is the probability you will LOSE?
I know how to use complement to get the answer. Why does P(Not face)* P(Not face) produce a different and wrong answer?
If both have to be face cards, then the probability of losing will include either the probability of one or both not being a face card.
P(face) * P(not face) + P(not face) * P(not face) = ?
Thank you. Now I know what I forgot. There are two ways of P(face)*P(not face) then add P(not face)* P(not face)
Went brain dead.
To answer this question, we need to calculate the probability of losing, which is the probability of not drawing two face cards in a row.
Using the complement rule, we can find the probability of not drawing a face card on the first draw and not drawing a face card on the second draw, denoted as P(Not face) * P(Not face).
However, this calculation yields the wrong answer because it assumes that the two events are independent. In reality, the probability of the second draw depends on the outcome of the first draw since the deck is not being replaced.
Let's break down the correct approach to calculate the probability of losing:
1. Probability of not drawing a face card on the first draw:
There are 40 non-face cards in a standard deck of 52 cards, so the probability of not drawing a face card on the first draw is P(Not face) = 40/52.
2. Probability of not drawing a face card on the second draw:
Since one card has already been drawn and not replaced, there are now 51 cards left in the deck, with 39 non-face cards remaining. Therefore, the probability of not drawing a face card on the second draw, given that a non-face card was drawn in the first draw, is P(Not face|Not face) = 39/51.
3. Probability of losing:
To find the probability of losing, we multiply the probabilities of the two events together:
P(Lose) = P(Not face) * P(Not face|Not face) = (40/52) * (39/51).
Calculating this expression yields the correct probability of losing. Using the complement rule would not give us the correct answer because it assumes independence between the two events, which is not the case here.