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)=(n(B))/(n(s)) \\ =(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)}=(4)/(52)+(4)/(52)-0 \\ =(8)/(52) \\ =(2)/(13) \end{gathered}`

The probability of getting jack or 4 is,

`(2)/(13)`