determine whether the following individual events are overlapping or non overlapping. then find the probability of the combined event.
drawing either a 7 or a spade from a regular deck of cards
The two individual events in this case are drawing a 7 and drawing a spade from a regular deck of cards.
To determine if these events are overlapping or non-overlapping, we need to check if both events can happen at the same time or not.
In this case, drawing a 7 and drawing a spade can happen at the same time. There is a possibility of drawing the 7 of spades, which satisfies both events. Therefore, these events are overlapping.
To find the probability of the combined event, we need to calculate the number of favorable outcomes (cards that are either a 7 or a spade) and divide it by the total number of possible outcomes (all the cards in the deck).
Number of favorable outcomes:
There are four 7s in a standard deck of 52 cards (7 of hearts, 7 of diamonds, 7 of clubs, and 7 of spades) and there are 13 spades in the deck. However, we already counted the 7 of spades as one of the favorable outcomes. So, we only need to consider the remaining 12 spades. Therefore, there are a total of 4 + 12 = 16 favorable outcomes.
Total number of possible outcomes:
There are 52 cards in a deck.
Probability of the combined event:
The probability of the combined event is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
P(7 or spade) = Number of favorable outcomes / Total number of possible outcomes
P(7 or spade) = 16 / 52
P(7 or spade) ≈ 0.3077 or 30.77%