we have a deck of 8 cards numbered from 1 to 8. some are grey and some are white, as shown below. the cards…

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

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

Answer

Answer:

(a) $\frac{4}{8}=\frac{1}{2}$ (b) $\frac{1}{4}$

Explanation:

Step1: Find total - white cards

There are 4 white cards (2, 3, 5, 7) out of 8 total cards for part (a). So probability $P(\text{white})=\frac{\text{Number of white cards}}{\text{Total number of cards}}=\frac{4}{8}=\frac{1}{2}$.

Step2: Find even - numbered and white cards

Even - numbered cards are 2, 4, 6, 8. Among them, only 2 is white. So given an even - numbered card is drawn, the probability $P(\text{white}|\text{even})=\frac{\text{Number of white and even cards}}{\text{Number of even cards}}=\frac{1}{4}$.