Question

A bowl has 8 green grapes and 15 red grapes. Henry randomly chooses a grape, eats it, and then chooses another grape. (a) What is the probability that both grapes are green? Show your work. (b) What is the probability that Henry eats a red grape then a green grape? Show your work. swer:​

Answer 1

(a) The probability that the first grape is green is 8/23. Since Henry does not replace the first grape, the probability that the second grape is also green is 7/22. Therefore, the probability that both grapes are green is:

P(both green) = P(first green) x P(second green | first green)

P(both green) = (8/23) x (7/22)

P(both green) = 0.115

So the probability that both grapes are green is 0.115.

(b) The probability that the first grape is red is 15/23. Since Henry does not replace the first grape, the probability that the second grape is green is 8/22. Therefore, the probability that Henry eats a red grape then a green grape is:

P(red then green) = P(first red) x P(second green | first red)

P(red then green) = (15/23) x (8/22)

P(red then green) = 0.184

So the probability that Henry eats a red grape then a green grape is 0.184.