Question

4.2 theoretical probability. calculating theoretical probabilities (deck of cards). if you randomly select a card from a well - shuffled standard deck of 52 cards, what is the probability that the card you select is a heart or 9? question help: video 1 video 2 message instructor

Explanation:

Step1: Calculate number of hearts

A standard deck has 13 hearts.

Step2: Calculate number of 9s

There are 4 cards with the number 9 in a deck.

Step3: Calculate number of 9 - of - hearts

There is 1 card which is both a heart and a 9.

Step4: Use the addition rule of probability

The formula for $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Here, $A$ is the event of getting a heart and $B$ is the event of getting a 9. The number of favorable outcomes for $A\cup B$ is $n(A\cup B)=13 + 4-1=16$.

Step5: Calculate the probability

The probability $P=\frac{n(A\cup B)}{n(S)}$, where $n(S) = 52$ (total number of cards in the deck). So $P=\frac{16}{52}=\frac{4}{13}$.

Answer:

$\frac{4}{13}$