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Vika
3 months ago
7

A box has 14 camera of which 6 are refurbished and 8 are new. If four of these 14 cameras are selected at random without replace

ment, what is the probability that (i) one new camera will be selected? (ii) at most one new camera will be selected?
Mathematics
1 answer:
Leona [12.6K]3 months ago
4 0

Answer:

160/1001, 175/1001

Step-by-step explanation:

i) We calculate:

₈C₁ methods to select 1 new camera from a selection of 8

₆C₃ methods to select 3 refurbished cameras from a selection of 8

₁₄C₄ methods to select 4 cameras from the total of 14 cameras

The probability formula is:

P = ₈C₁ ₆C₃ / ₁₄C₄

P = 8×20 / 1001

P = 160 / 1001

P ≈ 0.160

ii) For at most one new camera, it means we want either one new camera or none at all. We've calculated the probability of selecting one new camera already. The probability of not selecting any new camera is equivalent to selecting 4 refurbished cameras:

P = ₆C₄ / ₁₄C₄

P = 15 / 1001

Therefore, the combined probability is:

P = 160/1001 + 15/1001

P = 175/1001

P ≈ 0.175

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