Question

A company sells 14 types of crackers that they label varieties 1 through 14, based on spice level. What is the probability that the purchase results in a selection of a cracker with number less than or equal to 4, or a number greater than 10

Answer 1

`P(x\le 4\ or x> 10) = (4)/(7)` or
`P(x\le 4\ or x> 10) = 0.5714`

Explanation:

Given

`x = \{1,2,3,4,5,6,7,8,9,10,11,12,13,14\}`

Required

Determine
`P(x\le 4\ or x> 10)`

Because the events are independent, the probability can be solved using:

`P(A\ or\ B) = P(A) + P(B)`

So, we have:

`P(x\le 4\ or x> 10) = P(x \le 4) + P(x > 10)`

When
`x \le 4`, we have:
`x = \{1,2,3,4\}`

So:

`P(x \le 4) = (4)/(14)`

Also:

When
`x > 10`, we have:
`x = \{11,12,13,14\}`

So:

`P(x>10) =(4)/(14)`

`P(x\le 4\ or x> 10) = P(x \le 4) + P(x > 10)` becomes

`P(x\le 4\ or x> 10) = (4)/(14) + (4)/(14)`

`P(x\le 4\ or x> 10) = (4+4)/(14)`

`P(x\le 4\ or x> 10) = (8)/(14)`

`P(x\le 4\ or x> 10) = (4)/(7)`

`P(x\le 4\ or x> 10) = 0.5714`