Question

a card is drawn at random from a standard deck. Determine whether the events are mutually exclusive or not mutually exclusive. Then find each probability. P(jack or 4)

Answer 1

Mutually exclusive events:

Two events are mutually exclusive if they cannot occur at the same time.

There are 52 cards in a deck of cards.

n(s)=52.

Let A be event of getting jack.

n(A)=4.

So, Probability of getting jack is,

Let B be event of getting 4

n(B)=4.

So, Probability of getting 4 is,

$\begin{gathered} P(B)=\frac{n(B)}{n(s)} \\ =\frac{4}{52} \end{gathered}$

These two events do not occur at same time.

Therefore the events are mutually exclusive.

$P(A\cap B)=0$

To find the probability of getting jack or 4

$P(\text{A }\cup\text{B)}=P(A)+P(B)-P(A\cap B)$

hence,

$\begin{gathered} P(\text{A }\cup\text{B)}=\frac{4}{52}+\frac{4}{52}-0 \\ =\frac{8}{52} \\ =\frac{2}{13} \end{gathered}$

The probability of getting jack or 4 is,

$\frac{2}{13}$