Question

One card is drawn at random from the deck of cards shown. Which of the following probabilities is equal to one?

P(even or odd)
P(even and odd)
P(not yellow)

Answer 1

In your question where as one card is drawn at random form the deck of the cards and the ask is to find the probability that is equal to one and the answer is P(even or add). I hope you are satistfied with my answer and if you need some clarification, please feel free to ask for more

Answer 2

P(even or odd)

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) =
`P(A\cup B)`

using formula : [tex]P(A\cup B)= P(A)+P(B)-P(A\cap B)[/tex]

`P(even\cup odd)= P(even)+P(odd)-P(even\cap odd)`--(1)

So, we have already calculated the value of

`P(even)`

`P(odd)`

To calculate

`P(even\cap odd)` = P(even and odd)

But no card can be odd and even both

Thus,
`P(even\cap odd)` =0

putting all these value in (1)

⇒
`P(even\cup odd)= (1)/(2) +(1)/(2) -0`

⇒
`P(even\cup odd)= 1`

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