Question

The probability that a candidate secure a seat in engineering through EAMCET is 1/10. Seven candidates are selected at random from a center. The probability that exactly two will get seats is

A. 15(0.1)² (0.9)⁵
B. 20(0.1)² (0.9)⁵
C. 21(0.1)² (0.9)⁵
D. 23(0.1)² (0.9)⁵

Answer 1

The correct answer for the question is Option C. The probability of exactly two candidates securing seats in engineering through EAMCET can be calculated using the binomial distribution formula.

Step-by-step explanation:

The probability that exactly two candidates will secure seats in engineering through EAMCET can be calculated using the binomial distribution formula. The formula is:

P(X=k) = C(n,k) * p^k * (1-p)^(n-k)

Where:

• P(X=k) is the probability of getting exactly k successes (in this case, exactly 2 candidates securing seats).
• C(n,k) is the combination formula for selecting k out of n candidates.
• p is the probability of success (1/10 in this case).
• 1-p is the probability of failure (9/10 in this case).
• n is the total number of candidates selected (7 in this case).

Plugging in the values:

P(X=2) = C(7,2) * (1/10)^2 * (9/10)^5 = 21 * (0.1)^2 * (0.9)^5

Therefore, the correct answer is option C. 21(0.1)² (0.9)⁵.