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 club or a 9. Consider the given solution.
The first part of finding the probability considers using the formula for the probability of compound events. Here the formula was used incorrectly. The probability of the event of picking a club which is a 9 should be subtracted, not added. Consider the formula we should apply.
P(AorB)=P(A)+(B)-P(AandB)
In our case the event A is picking a club card, and event B is picking a 9. There are 13 club cards, and 4 9's in a deck of 52 cards. Also, there is 1 card which is both a club and a 9. We can use these to calculate the needed probabilities.
Event
Favorable Outcomes
Total
Probability
club
13
52
13/52
9
4
52
4/52
club and 9
1
52
1/52
Finally, we can substitute these values into the formula for the probability of compound events and simplify.
