Answer:
P(even or odd)
Step-by-step explanation:
Given : One card is drawn at random from the deck of cards (refer given figure)
Solution:
To find probability of getting even numbers
favorable events of even no. = {2,4,6,8,10} = 5
total events = {1,2,3,4,5,6,7,8,9,10} =10
Thus , probability of getting even numbers =
favorable events of even no. / total events
= 5/10 = 1/2
To find probability of getting odd numbers
favorable events of even no. = {1,3,5,7,9} = 5
total events = {1,2,3,4,5,6,7,8,9,10} =10
Thus , probability of getting odd numbers =
favorable events of odd no. / total events
= 5/10 = 1/2
Option A = P(even or odd) = [tex]P(A\cup B)[/tex]
using formula : [tex]P(A\cup B)= P(A)+P(B)-P(A\cap B)[/tex]
[tex]P(even\cup odd)= P(even)+P(odd)-P(even\cap odd)[/tex]--(1)
So, we have already calculated the value of
[tex]P(even)[/tex]
[tex]P(odd)[/tex]
To calculate
[tex]P(even\cap odd)[/tex] = P(even and odd)
But no card can be odd and even both
Thus, [tex]P(even\cap odd)[/tex] =0
putting all these value in (1)
⇒[tex]P(even\cup odd)= \frac{1}{2} +\frac{1}{2} -0[/tex]
⇒[tex]P(even\cup odd)= 1 [/tex]
Thus , P(even or odd) = 1
Now, consider Option 2 : P(even and odd)
Since no card can be odd and even both so P(even and odd) =0
Now, consider Option 3 : P(not yellow)
favorable event of not yellow = {1,2,3,4,5,7,8,9,10}=9
total events = {1,2,3,4,5,6,7,8,9,10} =10
Thus, P(not yellow) = 9/10
Hence OPTION A has probability equal to 1
