Question

We have a deck of 10 cards numbered from 1-10. Some are grey and some are white. The cards numbered are 1,2,3,5,6,8 and 9 are grey. The cards numbered 4,7, and 10 are white. A card is drawn at random. Let X be the event that the drawn card is grey, and let P(X) be the probability of X. Let not X be the event that the drawn card is not grey, and let P(not X) be the probability of not X.

Answer 1

Given:

The cards numbered are, 1,2,3,5,6,8, and 9 are grey.

The cards numbered 4,7 and 10 are white.

The total number of cards =10.

Let X be the event that the drawn card is grey.

P(X) be the probability of X.

Required:

We need to find P(X) and P(not X).

Step-by-step explanation:

All possible outcomes = All cards.

`n(S)=10`

Click boxes that are numbered 1,2,3,5,6,8, and 9 for event X.

The favourable outcomes = 1,2,3,5,6,8, and 9

`n(X)=7`

Since X be the event that the drawn card is grey.

The probability of X is

`P(X)=(n(X))/(n(S))=(7)/(10)`

Let not X be the event that the drawn card is not grey,

All possible outcomes = All cards.

`n(S)=10`

Click boxes that are numbered 4,7, and 10 for event not X.

The favourable outcomes = 4,7, and 10

`n(not\text{ }X)=3`

Since not X be the event that the drawn card is whic is not grey.

The probability of not X is

`P(not\text{ }X)=\frac{n(not\text{ }X)}{n(S)}=(3)/(10)`

Consider the equation.

`1-P(not\text{ X\rparen}`
`Substitute\text{ }P(not\text{ }X)=(3)/(10)\text{ in the equation.}`
`1-P(not\text{ X\rparen=1-}(3)/(10)`
`1-P(not\text{ X\rparen=1}*(10)/(10)\text{-}(3)/(10)=(10-3)/(10)=(7)/(10)`

`1-P(not\text{ X\rparen is same as }P(X).`

Final answer:

`1-P(not\text{ X\rparen is same as }P(X).`