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 21190 Start Fraction 21 over 190 End Fraction 776 Start Fraction 7 over 76 End Fraction 35 Start Fraction 3 over 5 End Fraction 780 Start Fraction 7 over 80 End Fraction
To calculate the probability of selecting an apple and a banana, we first need to find the total number of ways to choose 2 fruits out of 20 (5 bananas + 8 mangoes + 7 apples).
Total number of ways = 20 choose 2 = 20! / (2! * 18!) = 190
Next, we need to find the number of ways to select 1 apple and 1 banana out of 12 (5 bananas + 7 apples).
Number of ways to select 1 apple and 1 banana = 5 choose 1 * 7 choose 1 = 5 * 7 = 35
Therefore, the probability of selecting an apple and a banana is:
35 / 190 = 7 / 38
So, the correct answer is:
776 Start Fraction 7 over 76 End Fraction