Question

there are 6 white and 2 orange ping - pong balls in a brown paper bag. two balls are randomly chosen, one after the other without replacement. enter your answers as fractions or as decimals rounded to three decimal places. (the preview simply displays your answer in nice mathematical text. it does not mean that your answer is either right or wrong.) a) how many total balls are in the bag at the start? b) what is the probability that the 1st ball is orange? p(1st is orange)= c) what is the probability that the 2nd ball is also orange, given that the 1st ball was orange? p(2nd is orange | 1st is orange)= d) what is the probability that both the 1st and the 2nd balls are orange?

Explanation:

Step1: Calculate total balls

Add white and orange balls. $6 + 2=8$.

Step2: Calculate probability of 1st ball being orange

Number of orange balls divided by total balls. $\frac{2}{8}=\frac{1}{4}=0.250$.

Step3: Calculate probability of 2nd ball being orange given 1st is orange

After 1 orange ball is taken, there is 1 orange ball left and 7 total balls. So $\frac{1}{7}\approx0.143$.

Step4: Calculate probability of both balls being orange

Multiply probability of 1st being orange and 2nd being orange given 1st is orange. $\frac{2}{8}\times\frac{1}{7}=\frac{1}{28}\approx0.036$.

Answer:

a) 8
b) 0.250
c) 0.143
d) 0.036