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)
Responses
7/76
Start Fraction 7 over 76 End Fraction
3/5
Start Fraction 3 over 5 End Fraction
7/80
Start Fraction 7 over 80 End Fraction
21/190
Start Fraction 21 over 190 End Fraction
To calculate the probability of selecting an apple and a banana, we first need to find the total number of ways to select 2 fruits from the basket.
Total number of fruits = 5 (bananas) + 8 (mangoes) + 7 (apples) = 20 fruits
Total number of ways to select 2 fruits = 20C2 = (20!)/(2!(20-2)!) = 190
Next, we calculate the number of ways to select 1 apple and 1 banana.
Number of ways to select 1 apple out of 7 = 7C1 = 7
Number of ways to select 1 banana out of 5 = 5C1 = 5
Total number of ways to select 1 apple and 1 banana = 7 * 5 = 35
Therefore, the probability of selecting an apple and a banana = 35 / 190 = 7 / 38 = 21 / 190
So, the correct answer is 21/190.