Of the physics graduates at a university 30 receive a starti

Of the physics graduates at a university, 30% receive a starting salary of $60,000 or more. If five of the graduates are chosen at random, find the probability that all had a starting salary of $60,000 or more

Solution

Let x be the number of Physics graduates in the University. Then the number of Physics graduates in the University who are drawing a starting salary of $ 60000 or above is 30 % of x = 0.3x.

The probability of the 1st randomly chosen Physics graduate drawing a salary of $ 60000 or more is 0.3x/x = 1/3

The probability of the 2nd randomly chosen Physics graduate drawing a salary of $ 60000 or more is(0.3x -1)/(x -1)

The probability of the 3rd randomly chosen Physics graduate drawing a salary of $ 60000 or more is(0.3x -2)/( x - 2)

The probability of the 4th randomly chosen Physics graduate drawing a salary of $ 60000 or more is( 0.3x - 3)/(x -3)

The probability of the 5th randomly chosen Physics graduate drawing a salary of $ 60000 or more is( 0.3x -4)/(x- 4)

Therefore, the probability of all the 5 randomly chosen Physics graduate drawing a salary of $ 60000 or more is

1/3*[ (0.3x -1)/(x -1)]* [(0.3x -2)/(x -2)]*(0.3x -3)/(x -3)]* [(0.3x -4/(x -4)] = [( 0.3x - 1)(0.3x -2)(0.3x -3)(0.3x -4)] / [ ( 3(x -1)(x -2)(x -3)(x -4)]