Answer: [tex]\dfrac{18}{65}[/tex]
Step-by-step explanation:
Given : Fred spins a spinner with five equal spaces numbered 1 thru 5 and draws a card from a standard 52-card deck.
We know that the probability of each event is given by :-
[tex]\dfrac{\text{No. of favorable outcomes}}{\text{Total outcomes}}[/tex]
Event 1: He spins a 3.
Total outcomes for spinner with 5 equal section = 5
Then , the probability of spinning a 3 will be :-
[tex]P(E_1)=\dfrac{1}{5}[/tex]
Event 2: He draws a king.
No. of kings in a deck of cards = 4
Total number of cards in a deck of cards = 52
Then , the probability of getting a king will be :-
[tex]P(E_2)=\dfrac{4}{52}=\dfrac{1}{13}[/tex]
Since both events are independent then the probability he spins a 3 or draws a king will be the sum of probabilities each event .
[tex]i.e. \ P(E_1)+ P(E_2)\\\\=\dfrac{1}{5}+\dfrac{1}{13}=\dfrac{13+5}{65}=\dfrac{18}{65}[/tex]
Hence, the probability he spins a 3 or draws a king = [tex]\dfrac{18}{65}[/tex]
