Adiamond can be classified as either gem-quality or industrial-grade. 80% of diamonds are classified as industrial-grade.
(a) if two diamonds are chosen at random, what is the probability that both diamonds are industrial-grade?
(b) if seven diamonds are chosen at random, what is the probability that all seven diamonds are industrial-grade?
(c) what is the probability that at least one of seven randomly selected diamonds is gem-quality? would it be unusual that at least one of seven randomly selected diamonds is gem-quality?

a) 0.64

b) 0.21

c) 0.79

Step-by-step explanation:

Percentage of industrial-grade diamonds = 80%

This means, if one diamond is chosen at random, there is 80% chance that it will be of industrial-grade. So,

P(Industrial grade) = 80% = 0.80

Part a)

Probability that 1st diamond is industrial-grade = 0.80

Since, selection of diamonds in independent, the probability that 2nd diamond is also industrial grade = 0.80

The overall probability of both diamonds being industrial-grade will be the product of their individual probabilities, according to the fundamental rule of counting.

So, if two diamonds are chosen at random, the probability that both are industrial grade = 0.80 x 0.80 = (0.80)² = 0.64

Part b)

Following the same logic as we followed in the previous part.

The probability of each of the 7 diamonds being industrial-grade is 0.80, so the probability that all 7 are industrial grade will be:

Probability = 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 x 0.80 = = 0.21

So, if 7 diamonds are chosen at random, the probability that all 7 are industrial grade is 0.21.

Part c)

The event "at least one" is complement of event "none". So, the event "at least one of 7" will be complement of "none of the 7"

If none of the selected diamonds is gem quality, this means all 7 of the diamonds are industrial-grade. So,

The probability that none of the diamonds is gem-quality = The probability that all 7 are industrial-grade = 0.21

So,

The probability that at least one of the 7 selected diamonds is gem-quality = 1 - Probability that none is gem-quality

= 1 - 0.21

= 0.79

Since the probability that atleast one of the 7 randomly selected diamonds is gem-quality is greater than 0.05, it won't be unusual event.

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.

substitute,

circle 1 = 5

circle 2 = 20

circle 3 = 44

in this case no matter how you add, you will always get a perfect square..

hence proved

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