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.(1 point)
Options:
7/80
21/190
3/5
7/76
The probability of selecting an apple and a banana can be calculated as follows:
- The probability of selecting an apple first is 7/20 (since there are 7 apples out of 20 total fruits).
- After an apple is selected and removed, there are 19 fruits left, including 5 bananas. So the probability of selecting a banana second is 5/19.
- The probability of these two events happening in sequence is equal to the product of their probabilities: 7/20 * 5/19 = 7/76.
Therefore, the answer is option D) 7/76.
To calculate the probability of selecting an apple and a banana from the basket, we need to determine the probabilities of selecting an apple first and then a banana, or vice versa. Since there are 7 apples and 5 bananas in the basket, the probability of selecting an apple first is 7/20. After one apple is selected, there are 19 fruits remaining, including 5 bananas. Therefore, the probability of selecting a banana after an apple has been taken is 5/19.
Now, we can calculate the overall probability by multiplying the individual probabilities:
P(apple) * P(banana) = (7/20) * (5/19) = 35/380
Hence, the probability of selecting an apple and a banana is 35/380.