Question

A company has estimated that the probabilities of success for three products introduced in the market are 1/3, 2/5 and 2/3 respectively. assuming independence, find the probability that at least one product is successful.

A. 2/315​
B. 313​ /315
C. 8​/15
D. 7​/15

Answer 1

The probability of at least one product being successful is equal to 1 minus the probability of none of the products being successful. The answer is B. 13/15.

Step-by-step explanation:

To find the probability that at least one product is successful, we can use the complement rule. The probability of at least one product being successful is equal to 1 minus the probability of none of the products being successful.

Let's calculate the probability of none of the products being successful:

P(None of the products is successful) = (1 - 1/3)(1 - 2/5)(1 - 2/3)

= (2/3)(3/5)(1/3) = 6/45 = 2/15

Therefore, the probability of at least one product being successful is:

P(At least one product is successful) = 1 - P(None of the products is successful)

= 1 - 2/15 = 13/15

So the answer is 13/15.

Answer 2

The probability that at least one product is successful is found by subtracting the probability that none are successful from one. After calculating the probability that none are successful to be 2/15, subtracting this from 1 gives us 13/15, which is the correct answer.

Step-by-step explanation:

The question is asking for the probability that at least one product out of three is successful, given their respective probabilities of success and assuming that the events are independent. To find this, we can calculate the probability that none of the products are successful and then subtract this from 1. The probability of each product not being successful is 1 minus the probability of success:

• For the first product: 1 - 1/3 = 2/3
• For the second product: 1 - 2/5 = 3/5
• For the third product: 1 - 2/3 = 1/3

The probability that none of the products are successful (P(None)) is the product of these probabilities:

P(None) = (2/3) x (3/5) x (1/3) = 2/15

Therefore, the probability that at least one product is successful is:

P(at least one) = 1 - P(None) = 1 - 2/15 = 13/15

So the answer is: B. 13/15.