Probability of Selection Calculation
The problem asks for the probability that salesman A is selected when a three-member delegation is chosen from five salesmen (A, B, C, D, E).
Calculating Probability of A's Selection
We can find the probability that A is selected by first calculating the probability that A is *not* selected and then using the complement rule.
Consider the selection process step-by-step. There are 3 positions in the delegation.
- The probability that A is not chosen for the first position is $\frac{4}{5}$ (since there are 4 other salesmen).
- Given A was not chosen first, the probability that A is not chosen for the second position is $\frac{3}{4}$ (3 salesmen left out of 4 remaining).
- Given A was not chosen in the first two positions, the probability that A is not chosen for the third position is $\frac{2}{3}$ (2 salesmen left out of 3 remaining).
The overall probability that A is not selected is the product of these probabilities:
$P(\text{A not selected}) = \frac{4}{5} \times \frac{3}{4} \times \frac{2}{3}$
$P(\text{A not selected}) = \frac{24}{60} = \frac{2}{5}$
Now, we use the complement rule to find the probability that A *is* selected:
$P(\text{A selected}) = 1 - P(\text{A not selected})$
$P(\text{A selected}) = 1 - \frac{2}{5}$
$P(\text{A selected}) = \frac{5}{5} - \frac{2}{5} = \frac{3}{5}$
Therefore, the probability that salesman A gets selected is $\frac{3}{5}$.
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Important Questions from Probability
Two dice are thrown simultaneously. What is the probability of getting the same number on both the dice?
The probability of being 53 Sundays in year 2020 is-
Three dice are thrown randomly. The probability of coming 3 in at least one die is
The probability of having 53 Tuesdays in an ordinary year is:
When two dice are tossed simultaneously, the probability that the sum of the numbers appearing on both the dice is 8 will be
