Question

The contingency table represents a box of cards. Box of Cards 1 2 3 4 5 Total Black 1 1 1 1 1 5 Red 1 1 1 0 0 3 Total 2 2 2 1 1 8 What is the probability that a card chosen at random is black and 1?

Answer 1

Answer:

$Probability = \frac{1}{8}$

Step-by-step explanation:

Given

Box of Cards -- 1 -- 2 -- 3 -- 4 -- 5 -- Total

Black --------------1 ---1 ----1 ----1 ---1 ----5

Red ---------------- 1 ---1 ----1 ----0--- 0--- 3

Total --------------- 2 ---2 --2-----1 -----1 ---8

Required

Determine the probability of a card being black and being card 1

To solve this, we the the number of card 1 that is black

This is shown below

Box of Cards -- 1

Black --------------1

This implies that, 1 card is black and also card 1

Represent this with $n(Black\ and\ 1)$

$n(Black\ and\ 1) = 1$

Next, is to get the total number of cards

From the given parameters;

$Total = 8$

The probability is calculated as follows

$Probability = \frac{n(Black\ and\ 1)}{Total}$

$Probability = \frac{1}{8}$