Question

a box contains 8 good and 2 bad oranges. 3 of the oranges are selected at random one after the other with replacement. what is the probability that none is bad​

Answer 1

The probability of selecting a good orange on the first draw is 8/10, since there are 8 good oranges out of 10 total oranges.

Since each drawing is done with replacement, the probability of selecting a good orange on the second draw is also 8/10.

Similarly, the probability of selecting a good orange on the third draw is also 8/10.

The probability of none of the oranges being bad is the product of the probabilities of each individual draw being good:

P(none_bad) = P(good_1) * P(good_2) * P(good_3)

= 8/10 * 8/10 * 8/10

= 0.512

Therefore, the probability that none of the oranges selected are bad is 0.512 or 51.2%.