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Naily [24]
3 years ago
6

Adam goes to the grocery store to buy cereal. the shelves contain 9 boxes of Brand A and 6 boxes of Brand B. He selects one bran

d at random and then put it back. Another person does the same thing. What is the probability they both selected Brand A?
Mathematics
1 answer:
Paladinen [302]3 years ago
7 0

We can first find the probability of the first person picking Brand A, which would be:

9/6+9

=9/15

=3/5

We can then find the probability of the second person choosing brand A:

(9-1)/(6+9-1)

=8/14

To find the probability they both select Brand A, we could multiply them together:

3/5 x 8/14

=12/35

Therefore the answer would be 12/35.

Hope it helps!


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(a)See below

(b)I) 0.125  (ii)0.828125   (iii)0.234375   (iv) 0.625   (v)0.65625

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When an  8-sided die is rolled twice, the sample space is the set of all possible pairs (a,b) where a is the 1st outcome and b is the 2nd outcome.

The sample space is:

[(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),(1, 7),(1, 8)\\(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),(2, 7),(2, 8)\\(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),(3, 7),(3, 8)\\(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),(4, 7),(4, 8)\\(5, 1), (5, 2), (5, 3), (5, 4), (5, 5),(5, 6),(5, 7),(5, 8)\\(6, 1), (6, 2), (6, 3), (6, 4)(6, 5),(6, 6),(6, 7),(6, 8)\\(7, 1), (7, 2), (7, 3), (7, 4)(7, 5),(7, 6),(7, 7),(7, 8)\\(8, 1), (8, 2), (8, 3), (8, 4)(8, 5),(8, 6),(8, 7),(8, 8)]

<u>PART A</u>

The sample space of the product a*b of each pair forms the required possibility diagram.

This is given as:  

1, 2, 3, 4, 5, 6,7,8\\2, 4, 6, 8, 10, 12,14,16\\3,6,9,12,15,18,21,24\\4,8,12,16,20,24,28,32\\5,10,15,20,25,30,35,40\\6,12,18,24,30,36,42,48\\7,14,21,28,35,42,49,56\\8,16,24,32,40,48,56,64

<u>PART B</u>

I) A prime number

The number of products that gives prime numbers = 8  

The probability that the product is a prime number

=\dfrac{8}{64}= \dfrac{1}{8}\\=0.125

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Number of products that results in perfect squares =11

The probability that the product is not a perfect square

=\dfrac{64-11}{64}= \dfrac{53}{64}\\=0.828125

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Number of products that are multiples of 5=15

 The probability that the product is a multiple of 5

=\dfrac{15}{64}\\=0.234375

iv) Less than or equal to 21

Number of products which are less than or equal to 21=40

 The probability that the product less than or equal to 21

=\dfrac{40}{64}=\dfrac{5}{8}\\=0.625

v) Divisible by 4 or 6

Number of products divisible by 4 or 6= 42

 The probability that the product is divisible by 4 or 6

=\dfrac{42}{64}=\dfrac{21}{32}\\=0.65625

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Answer:

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