Question

A jewelry supplier has a supply of pairs of earrings of which 40% are platinum pairs. a jewelry store orders five sets of earrings from this supplier. if the supplier selects the pairs of earrings at random, what is the chance that the jewelry store gets exactly two sets of platinum pairs?

Answer 1

The chance that the jewelry store gets exactly two sets of platinum pairs = 0.3456

Explanation:

A jewelry supplier has a supply of pairs of earrings of which 40% are platinum pairs

⇒ The probability that the selected pair of earrings will be platinum = 0.4

⇒ The probability of success, p = 0.4

So, The probability of failure, q = 1 - 0.4 = 0.6

Now, we need to choose 2 pair of earrings among 5 pair of earrings

So, n = 5 , r = 2

`\text{Required Probability = }_r^n\txterm C* (p)^r* (q)^(n-r) \\\\\implies \text{Required Probability = }_2^5\txterm C* (0.4)^2* (0.6)^3\\\\\implies \text{Required Probability = }10* 0.03456\\\\\implies \text{Required Probability = }0.3456`

Hence, the chance that the jewelry store gets exactly two sets of platinum pairs = 0.3456

Answer 2

There would be about a 3.45% chance of getting a combination of 2 platinum and 3 others.

We can find this by recognizing that the odds for a non-platinum pair is 60% and the platinum pair is 40%. In order to find the likelihood, we would have to multiply the odds for each selection.

This would give us 60%*60%*60%*40%*40% = 3.45%.