How do I find P(heart or red) in four decimal places

Question

P(heart or red)=

Answer 1

Answer: P(Heart or Red)=1/2

Explanation:

P(Heart or Red) represents the statement, "the probability of drawing a heart or a red card". Whenever we see "or" in probability, we think the union. Hence, we are interested in calculating the probability of the union of the two events: drawing a heart and drawing a red card.

If we consider a standard deck of 52 cards, we know that 13 are hearts and 26 are red. Therefore, we have the following two probabilities:

P(Heart) = 13/52 = 1/4

P(Red) = 26/52 = 1/2

We also know that the probability of drawing a heart changes depending on the color of the card we select. If we select a black card, then the probability of drawing a heart is zero; however, if we draw a red card, then the probability of drawing a heart is 1/2.

Why is the probability the card is a heart given we drew a red card equal to 1/2?

Of the 26 red cards in the deck, 13 of them are hearts, so the probability that we drew a heart given the card drawn is red is 13/26 = 1/2.

Using the conditional probability formula, we can calculate the probability of selecting a red card that is also a heart:

P(Heart and Red) = P(Heart | Red)P(Red) = (1/2)*(26/52) = 13/52 = 1/4. P(Heart | Red) is the conditional probability of drawing a heart given a red card is drawn.

Finally, to calculate the probability of the union of these two events, we use:

P(Heart or Red) = P(Heart) + P(Red) - P(Heart and Red) = 1/4 + 1/2 - 1/4 = 1/2.