Analyze the given solution step by step. What is the formula we use when we want to calculate the probability of compound events?
Error: Wrong formula. Forgot to subtract P(heart and face card). Correction: P(heart)+P(face card)-P(heart and face card)= 1126
Practice makes perfect
We want to describe and correct the error made in finding the probability of randomly drawing the given card from a standard deck of 52 cards. First we will analyze the probability of drawing a card that is a heart or a face card. Consider the given solution.
The first part of finding the probability considers using the formula for the probability of compound events. The formula which was used here is correct only for disjoint events. However, note that the events of picking a heart card and picking a face card are not disjoint, since we can pick for example a queen of hearts. Consider the formula we should apply.
P(AorB)=P(A)+(B)-P(AandB)
In our case event A is picking a heart card, and event B is picking a face card. There are 13 heart cards, and 12 face cards in a deck of 52 cards. Also, there are 3 cards which are both face cards and heart cards. We can use these to calculate the needed probabilities. Recall that probability is a quotient of the favorable outcomes and all possible outcomes.
Event
Favorable Outcomes
Total
Probability
heart card
13
52
13/52
face card
12
52
12/52
heart and face card
3
52
3/52
Finally, we can substitute these values into the formula for the probability of compound events and simplify.
P(heart or face card)=P(heart)+P(face card)-P(heart and face card)
