Question

The sample space is orange, purple, and white. If P(Orange )=2/5 and P(purple) = 3/10 what is P=(white)

Answer 1

`(3)/(10)`

Explanation:

Probability refers to chance of occurrence of an event .

Formula of probability :

Probability = No. of favourable outcomes / Total no. of outcomes

Let
`E_1\,,\,E_2\,,\,E_3\,,...` be the events and S denotes the sample space .

Properties of Probability :

1 .
`\sum_(i=1)^(n)P(E_i)=1`

2.
`0\leq P(E_i)\leq 1`

Given :

P(Orange) = 2/5

P(purple) = 3/10

We know that P(Orange ) + P(purple) + P(white) = 1

So,

`(2)/(5)+(3)/(10) +` P(white) = 1

On transposing 2/5 and 3/10 on RHS , we get

P(white) =
`1-(2)/(5)-(3)/(10)=(10-4-3)/(10)=(3)/(10)`

Answer 2

White would be 3/10. Since orange is 2/5, it can also be written as 4/10 since 4/10 simplified would be 2/5. Also since you know purple is 3/10, so you must add what you know to get what you don't know. Orange 4/10 plus purple 3/10 would be 7/10. You would then subtract what the whole thing is worth which is 10/10. 10/10 minus 7/10 would be 3/10 which is the remainder of what is left which is white.