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

Answer:

$P(x\le 4\ or x> 10) = \frac{4}{7}$ or $P(x\le 4\ or x> 10) = 0.5714$

Step-by-step 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:

$P(x \le 4) = \frac{4}{14}$

Also:

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

So:

$P(x>10) =\frac{4}{14}$

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

$P(x\le 4\ or x> 10) = \frac{4}{14} + \frac{4}{14}$

$P(x\le 4\ or x> 10) = \frac{4+4}{14}$

$P(x\le 4\ or x> 10) = \frac{8}{14}$

$P(x\le 4\ or x> 10) = \frac{4}{7}$

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