Because of a mistake in packaging, a case of 16 bottles of wine contained 9 of brand A and 7 of brand B, each without labels. All the bottles look alike and have an equal probability of being chosen. FiveFive bottles are randomly selected. (a) What is the probability that all fivefive are brand A? (b) What is the probability that exactly twotwo areare brand A? (c) What is the probability that none is brand A?

a) 0.0289

b) 0.289

c) 0.0048

Step-by-step explanation:

16 bottles total

9 Brand A

7 Brand B

5 bottles selected

(a) What is the probability that all five are brand A?

Total: ₁₆C₅ = 4368

5 bottles brand A

₉C₅ = 126

126/4368 = 0.0289

(b) What is the probability that exactly two are brand A?

Total: ₁₆C₅ = 4368

2 of Brand A: ₉C₂ = 36

3 of Brand B: ₇C₃ = 35

As we have 2 of A AND 3 of B = 36*35 = 1260

1260/4368 = 0.289

(c) What is the probability that none is brand A?

Total: ₁₆C₅ = 4368

5 of Brand B: ₅C₇ = 21

21/4368 = 0.0048