Question

we have a deck of 8 cards numbered from 1 to 8. some are white and some are grey, as shown below. the cards numbered 1, 2, 4, 5, 6, 7, and 8 are white. the card numbered 3 is grey. answer the following questions. write each answer as a fraction. a card will be drawn at random. (a) what is the probability that the number 4 card is drawn? (b) what is the probability that the number 4 card is drawn, given that the card drawn is white?

Explanation:

Step1: Define total and favorable outcomes

Total cards: 8, favorable (card 4): 1
Probability = $\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{1}{8}$

Step2: Define conditional total and favorable

White cards: 7, favorable (white card 4): 1
Conditional Probability = $\frac{\text{Favorable White Outcomes}}{\text{Total White Outcomes}} = \frac{1}{7}$

Answer:

(a) $\frac{1}{8}$
(b) $\frac{1}{7}$