Question

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?

Answer 1

Answer:

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