Question

The probability of selection of three candidates a,b and c in an organization is 2/5,5/6 and 4/7 respectively.Find the probability that at least one of them get selected.

Answer 1

Answer:

The probability that none will be selected is:

3/5 * 1/6 * 3/7 = 9 / 210 = 3 / 70

Therefore the probability that one or more will be selected is:

1 - 3 / 70 = 67 / 70

Answer 2

Probability that at least one of them get selected is 67/70.

Given:

• The probability of selection of three candidates a,b and c in an organization is 2/5,5/6 and 4/7 respectively.

To find:

• Find the probability that at least one of them get selected.

Solution:

Formula to be used:

• Probability of atleast one selection:1- Probability of no selection.
• Probability of not selection: 1- probability of selection

Step 1:

Let the probability of selection of a,b and c are P(a),P(b), and P(c) respectively.

$P(a) = \frac{2}{5} ,P(b) = \frac{5}{6} , and \: P(c) = \frac{4}{7}$

Step 2:

Find the probability of not selection of a,b and c respectively.

$\bf P( \bar a),P(\bar b), and \: P( \bar c)$

Thus,

$P( \bar a) = \frac{3}{5} ,P(\bar b) = \frac{1}{6} , and \: P( \bar c) = \frac{3}{7}$

Thus,

Probability of no selection:

$P( \bar a\bar b\bar c) = \frac{3}{5} \times \frac{1}{6} \times \frac{3}{7}$

or

$\bf P( \bar a\bar b\bar c) = \frac{3}{70}$

Step 3:

Find the probability that at least one of them get selected.

Let the probability that at least one of them get selected is given by P(abc);

$P(abc) = 1 - P( \bar a\bar b\bar c)$

or

$P(abc) = 1 - \frac{3}{70}$

or

$\bf \red{P(abc) = \frac{67}{70}}$

Thus,

Probability that at least one of them get selected is 67/70.

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