We select a card at random from a set that contains four suits, each of which consists of cards numbered from 1 to 10.
We are asked to find the probability that we select a red card or a card greater than 5. Note that we can choose a card that is both red and greater than 5. Since the events have an outcome in common, they are overlapping events. Let's recall the formula for P( Aor B) when A and B are overlapping events.
P( Aor B)=P( A)+ P( B)-P( Aand B)
In order to find the desired probability, we will find the individual probabilities and the probability that we select a card that is both red and greater than 5. Let's start by calculating the probability of choosing a red card.
Out of 40 cards, there are 10 red cards.
P( red card)= 10/40=1/4
Next, we will calculate the probability of choosing a card greater than 5.
Out of 40 cards, there are 20 cards greater than 5.
P( card greater than5)= 20/40=1/2
Now we will calculate the probability of both choosing a red card and choosing a card greater than 5.
Out of 40 cards, there are 5 red cards greater than 5.
P( red cardand card greater than5) = 5/40 = 1/8
Finally, we can find the desired probability.
