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.
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%.
To calculate the probability of selecting an apple and a banana, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of fruits = 5 bananas + 8 mangoes + 7 apples = 20 fruits
When one fruit is selected, there are 20 - 1 = 19 fruits remaining in the basket.
The probability of selecting an apple as the first fruit is 7/20, since there are 7 apples out of 20 fruits.
After selecting the first fruit, there are 19 fruits remaining in the basket, with 5 bananas among them.
The probability of selecting a banana as the second fruit is 5/19, since there are 5 bananas out of the 19 remaining fruits.
To calculate the probability of both events happening (selecting an apple and a banana), we multiply the probabilities:
P(apple and banana) = P(apple) * P(banana|apple selected)
= (7/20) * (5/19)
= 35/380
Therefore, the probability of selecting an apple and a banana from the basket is 35/380 or approximately 0.0921.