Determine whether the following individual events are overlapping or non-overlapping. Then find the probability of the combined event.
Drawing either a face card or a heart from a regular deck of cards
The individual events in this case are:
1. Drawing a face card
2. Drawing a heart
These events are non-overlapping because a face card (jack, queen, or king) is not a heart.
To find the probability of the combined event (drawing either a face card or a heart), we need to find the probabilities of each individual event and add them together.
1. Probability of drawing a face card:
There are 12 face cards in a deck (4 jacks, 4 queens, and 4 kings) and a total of 52 cards in a deck. Therefore, the probability of drawing a face card is 12/52, which simplifies to 3/13.
2. Probability of drawing a heart:
There are 13 hearts in a deck and a total of 52 cards, so the probability of drawing a heart is 13/52, which simplifies to 1/4.
To find the probability of the combined event (drawing either a face card or a heart), we add the probabilities of the individual events:
P(face card or heart) = P(face card) + P(heart)
= 3/13 + 1/4
= 12/52 + 13/52
= 25/52
Therefore, the probability of drawing either a face card or a heart from a regular deck of cards is 25/52, which simplifies to 5/13.