Question

The director of a film festival received 9 submissions, 7 of which were sci-fi films. If the director randomly chose to play 6 of the submissions on the first day of the festival, what is the probability that all of them are sci-fi films? Write your answer as a decimal rounded to four decimal places .

Answer 1

Given data:

9 submissions out of which 7 were sci-fi

If the director randomly chose to play 6 of the submissions on the first day of the festival

Then, the probability that all of them are sci-fi films will be obtained as follows

At the first selection, it will be: 7/9

At the second selection, it will be: 6/8

At the third selection, it will be: 5/7

At the fourth selection, it will be: 4/6

At the fifth selection, it will be: 3/5

At the sixth selection, it will be: 2/4

Thus, the probability will be

`(7)/(9)*(6)/(8)*(5)/(7)*(4)/(6)*(3)/(5)*(2)/(4)=(5040)/(60480)`

=>

`(5040)/(60480)=(1)/(12)`

=>

`(1)/(12)=0.0833`

Answer = 0.0833