Did I do this problem right?
Consider the experiment of drawing two cards without replacement from an ordinary deck of playing cards. What are the odds in favor of drawing a spade or a heart?
Answer: P(Spade)*P(Spade)=(13/52)x(13/51)=169/2652=0.06372. Is this right?
Thanks.
No, you did the probability of drawing two spades. As I read the question, you want the probabilitiy of one spade or one heart,
Pr= Pr(one spade and one club/diamond)+pr(heart and one club/diamond).
Pr=13/52* 26/51 + 13/52*26/51
check my thinking.
So, do I multiply 13/52*26/51 for both and then add?
Ex: 13/52*26/51+13/52*26/51=
338/2652+338/2652=
676/2652
Is this right?
Thanks.
Did I do the problem right? Was the answer 676/2652?
Thanks.
Yes, your calculations are incorrect. To find the odds in favor of drawing a spade or a heart, we need to consider the favorable outcomes and divide it by the total number of equally likely outcomes.
First, let's determine the number of favorable outcomes. We want to calculate the probability of drawing a spade or a heart, which means we need to find the number of spades and the number of hearts in the deck.
The deck contains 52 cards, with 13 cards in each suit (spades, hearts, diamonds, and clubs). Since we are drawing two cards without replacement, we need to consider two scenarios:
Scenario 1: Drawing a spade and then a heart
The probability of drawing a spade on the first draw is 13/52 since there are 13 spades in the deck. After drawing a spade, there are 51 cards remaining, including 13 hearts. Therefore, the probability of drawing a heart on the second draw, given that we already drew a spade, is 13/51.
To calculate the probability of both events happening (drawing a spade and then a heart), we multiply the probabilities:
P(Spade and then Heart) = (13/52) * (13/51)
Scenario 2: Drawing a heart and then a spade
This scenario is similar to the first scenario, but we interchange the probabilities of drawing a spade and a heart:
P(Heart and then Spade) = (13/52) * (13/51)
Now, we need to add the probabilities of these two scenarios since we want the odds in favor of drawing a spade or a heart:
P(Spade or Heart) = P(Spade and then Heart) + P(Heart and then Spade)
Therefore,
P(Spade or Heart) = (13/52) * (13/51) + (13/52) * (13/51)
Simplifying the expression, we get:
P(Spade or Heart) = 169/2652 = 0.06369 (approximately)
So, the correct probability is approximately 0.06369, which is equivalent to 169/2652.