Mutually exclusive or not? Not mutually exclusive. Probability: 413 or about 30.8 %
Practice makes perfect
We want to determine whether the events are mutually exclusive and find the probability of their union. We will do these things one at a time.
Mutually Exclusive
Events that cannot occur at the same time are mutually exclusive. Mutually exclusive events have no outcomes in common. For example, because it is not possible to toss a coin and obtain heads and tails at the same time, these two events are mutually exclusive.
Rules for Probability
If A and B are mutually exclusive events, the probability that A and B will occur is P(AandB)=0.
If A and B are not mutually exclusive events, the probability that A and B will occur is P(AandB)≠0.
One out of the four aces is a heart, so it is possible to be both an ace and a heart in the given deck. Therefore, A and B are not mutually exclusive events.
Probability
Now, we can find the probability that the card drawn is either an ace or a heart.
Addition Rules for Probability
If A and B are mutually exclusive events, the probability that A or B will occur is P(AorB)=P(A)+P(B).
If A and B are not mutually exclusive events, the probability that A or B will occur is P(AorB)=P(A)+P(B)-P(AandB).
We know that there are 52 cards in the deck. Out of these, 4 cards are aces, 13 cards have a heart suit, and only 1 card is the ace of hearts.
Next, we can calculate P(A), P(B), and P(AandB).
P(A)&=4/52 l← ← lAces Total cards [0.5em]
P(B)&=13/52 l← ← lHearts Total cards [0.5em]
P(AandB)&=1/52 l← ← lAce of hearts Total cards
Finally, considering that A and B are not mutually exclusive events, let's calculate P(AorB).
