Question

Debbie randomly selects a card from a standard deck. What is the probability that either a heart or a Queen is selected?

Answer 1

See explanation.

Explanation:

We are looking for the probability that either of 2 events occur, so we have to use the formula:

`P(HuuQ)=P(H)+P(Q)-P(HnnQ)`

The formula cones from the fact that if we only add two probabilities, we count all events in their intersection twice. In our example we count choosing the queen of hearts once as choosing heart, and once as choosing the queen, so to calculate the actual probability we have to subtrat all events counted twice (i.e. the intersection of 2 events).

Here we have:

`P(H)=13/52` because there are 13 cards of each suit in the deck.

`P(Q)=4/52` because there are 4 queens (one for each suit)

`P(HnnQ)=1/52` there is one card which is both a queen and a heart (i.e. the queen of hearts)

Finally we get:

`P(HuuQ)=13/52+4/52-1/52=16/52=4/13`