According to a recent student poll, 5/7 out of 21 members of

[BTGmoderatorLU]

Source: Veritas Prep

According to a recent student poll, \(\frac{5}{7}\) out of 21 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking?

A. \(\frac{1}{14}\)
B. \(\frac{4}{49}\)
C. \(\frac{2}{7}\)
D. \(\frac{45}{49}\)
E. \(\frac{13}{14}\)

The OA is E

[deloitte247]

Given that 5/7 of 21 is interested in banking.
$$\frac{5}{7}\cdot21=15$$
So, 15/21 is interested in investment banking while 6 are NOT interested in investment banking.
But, we are asked to select 2 at random.
Using the logical inverse of at least one = none at all
Probability of "at least 1" want investment banking = PA
The probability that 2 do not want investment banking = P(Not A)
$$1-P\left(Not\ A\right)=PA$$
P(Not A) = Probability Inverse = (probability that 1 do not want banking) * (probability that 2 do not want banking)
$$=\frac{6}{21}\cdot\frac{5}{20}=\frac{30}{420}=\frac{3}{42}=\frac{1}{14}$$
$$PA=1-P\left(Not\ A\right)$$
$$PA=\frac{1}{1}-\frac{1}{14}=\frac{14-1}{14}=\frac{13}{14}$$

Answer = option E

[swerve]

15 students are interested, 6 are not interested

Prob \(= 1 - \frac{6C_2}{21C_2} = 1 - \frac{6\cdot 5}{21\cdot 20}=1 - \frac{1}{14} = \frac{13}{14}\,\Rightarrow\) __E__

[Scott@TargetTestPrep]

Source: Veritas Prep

According to a recent student poll, \(\frac{5}{7}\) out of 21 members of the finance club are interested in a career in investment banking. If two students are chosen at random, what is the probability that at least one of them is interested in investment banking?

A. \(\frac{1}{14}\)
B. \(\frac{4}{49}\)
C. \(\frac{2}{7}\)
D. \(\frac{45}{49}\)
E. \(\frac{13}{14}\)

The OA is E

We can use the equation 1 - P(none interested in banking) = P(at least one is interested in banking)

First, we see that 5/7 x 21 = 15 are interested in banking, so 6 aren't interested in banking and thus:

P(none interested in banking) = 6/21 x 5/20 = 2/7 x 1/4 = 2/28 = 1/14

Thus, P(at least one is interested in banking) = 1 - 1/14 = 13/14.

Answer: E