A basket of fruits contains 5 bananas, 8 mangoes, and 7 apples. Two fruits are randomly selected without replacement. Calculate the probability of selecting an apple and a banana.

Answer 1

There are a total of 20 fruits in the basket.

The probability of selecting an apple on the first pick is 7/20 since there are 7 apples out of 20 total fruits.

After one fruit has been selected, there are 19 fruits left in the basket. The probability of selecting a banana (assuming an apple was selected first) is 5/19 since there are 5 bananas left out of 19 fruits.

Therefore, the probability of selecting an apple and a banana in that order is:

P(apple then banana) = (7/20) * (5/19) = 0.092

However, it doesn't matter which order we select the fruits in since the question doesn't specify. So we also need to calculate the probability of selecting a banana first and then an apple:

P(banana then apple) = (5/20) * (7/19) = 0.092

The probability of selecting either an apple and a banana (in any order) is the sum of these two probabilities:

P(apple and banana) = P(apple then banana) + P(banana then apple)

P(apple and banana) = 0.092 + 0.092 = 0.184

Therefore, the probability of selecting an apple and a banana from the basket of fruits is 0.184 or 18.4%.