Question

Candidates for a job are interviewed one by one until a qualified candidate is found. Thirty percent of the candidates are qualified. a. What is the probability that the first candidate is qualified? b. What is the probability that the first candidate is unqualified and the second candidate is qualified? c. Let X represent the number of candidates interviewed up to and including the first qualified candidate. Find PIX= 4).

Answer 1

The probability that the first candidate is qualified is 30%. The probability that the first candidate is unqualified and the second candidate is qualified is 21%. The probability that the number of candidates interviewed up to and including the first qualified candidate is 4 is 17.1%.

Step-by-step explanation:

a. The probability that the first candidate is qualified is 30% or 0.3.

b. To find the probability that the first candidate is unqualified and the second candidate is qualified, we multiply the probability of the first candidate being unqualified (70% or 0.7) by the probability of the second candidate being qualified (30% or 0.3). So the probability is 0.7 x 0.3 = 0.21 or 21%.

c. Let X represent the number of candidates interviewed up to and including the first qualified candidate. To find the probability that X = 4, we need to calculate the probability of interviewing 3 unqualified candidates followed by 1 qualified candidate. The probability of an unqualified candidate being selected is 70% or 0.7, and the probability of a qualified candidate being selected is 30% or 0.3. So the probability is (0.7)^3 x 0.3 = 0.171 or 17.1%.

Answer 2

The probability that the first candidate is qualified is 30%. The probability that the first candidate is unqualified and the second is qualified is 21%. The probability that the fourth candidate is the first qualified one is 10.29%.

Step-by-step explanation:

The probability that the first candidate interviewed is qualified is simply the percentage of candidates that are qualified, which is 30% or 0.30.

The probability that the first candidate is unqualified and the second candidate is qualified involves two steps: firstly, the first candidate being unqualified, which has a probability of 70% or 0.70, and secondly, the second candidate being qualified, with a probability of 30% or 0.30. To find the joint probability of both events happening, we multiply them: 0.70 * 0.30 = 0.21 or 21%.

To find the probability that the first qualified candidate is the fourth one interviewed (P(X = 4)), we must consider that the first three candidates are unqualified, and the fourth is qualified. This can be calculated using the geometric distribution formula: (0.70)3 * (0.30) = 0.1029 or 10.29%.