Two cards are drawn without relplacement from a shuffled deck of 52 cards. Determine the probability of each event.
a)The first card is a heart and the second card is Q of hearts.
P(BlA)=P(A&B)/P(A)
(13/52)(1/51)/(1/4) = 1/51
How is this method incorrect?
I don't see why you are using the Conditional probability formula on this one.
you want the event to happen in a specific order, namely
one of the non-queen hearts, and then the queen of hearts.
so
prob = 12/52 * 1/51 = 1/121
In order for the second card to be the queen of hearts, the first card must be some other heart, and that has a probability of 12/52 = 3/13. Multiply that by the prob. of getting QH on the next draw, which is 1/51, and you get
3/663 = 1/221
Whatever you are doing with Bayesian probabilities P(B|A), etc., is wrong.
1/51 is the probability of getting QH on the second draw, after getting ANYTHING ELSE on the first draw.
I was just taught this formula so I thought I'd use it, since one event comes after another.
Thank you.
The method you provided is incorrect because it assumes that the events are independent, meaning that the outcome of one event does not affect the outcome of the other. In this case, the events are not independent because the second event depends on the outcome of the first event.
To calculate the probability correctly, you should consider the concept of conditional probability, which takes into account the information from the first event.
Let's break down the calculation step by step:
a) The first card is a heart and the second card is the Q of hearts.
To calculate the probability of event A (the first card is a heart), we need to determine the number of favorable outcomes (heart cards) and divide it by the total number of possible outcomes (all 52 cards). There are 13 hearts in a deck of 52 cards, so P(A) = 13/52 = 1/4.
Now, for event B (the second card is the Q of hearts), we need to take into account the information that the first card was already drawn and it was a heart. After the first card is drawn, there are 51 cards left, and only one of them is the Q of hearts. So P(B|A) = 1/51, meaning the probability of event B given event A has occurred.
Finally, to calculate the probability of both events happening together, we multiply the individual probabilities: P(A and B) = P(A) * P(B|A) = (1/4) * (1/51) = 1/204.
Therefore, the correct probability for the event "the first card is a heart and the second card is the Q of hearts" is 1/204.