A single card is pulled from a deck of cards. The probability that the card is black in colour or is an ace is:
To find the probability that the card is black in colour or is an ace, we need to calculate the sum of the probabilities of these two mutually exclusive events.
1. Probability of drawing a black card:
In a standard deck of 52 cards, there are 26 black cards (13 clubs and 13 spades). Therefore, the probability of drawing a black card is 26/52 = 1/2.
2. Probability of drawing an ace:
In a standard deck of 52 cards, there are 4 aces (one for each suit - hearts, clubs, diamonds, and spades). Therefore, the probability of drawing an ace is 4/52 = 1/13.
Since these two events are mutually exclusive (a card cannot be both black and an ace), we can add their probabilities together to find the probability of either event occurring:
Probability (black card or ace) = Probability (black card) + Probability (ace)
= (1/2) + (1/13)
= 13/26 + 2/26
= 15/26
Therefore, the probability that the card drawn is black in colour or is an ace is 15/26.
To find the probability that the card is black in color or is an ace, we need to find the probability of each event occurring individually and then add them together.
1) Probability of the card being black:
A standard deck of cards has 26 black cards out of a total of 52 cards (clubs and spades are black). Therefore, the probability of pulling a black card is 26/52, which simplifies to 1/2.
2) Probability of the card being an ace:
A standard deck of cards has 4 aces out of a total of 52 cards. Therefore, the probability of pulling an ace is 4/52, which simplifies to 1/13.
3) Probability of the card being black or an ace:
To find the probability of both events happening together, we need to add the probabilities of both individual events and then subtract the probability of them happening at the same time (to avoid double-counting).
Prob(black or ace) = Prob(black) + Prob(ace) - Prob(black and ace)
Prob(black and ace) = Prob(black) * Prob(ace) = (1/2) * (1/13) = 1/26
Prob(black or ace) = (1/2) + (1/13) - (1/26)
= 13/26 + 2/26 - 1/26
= 14/26
= 7/13
So, the probability that the card is black in color or is an ace is 7/13.