Question

Assume red and green are equally likely occurrences. Using Pascal’s triangle, what is the probability that you will get one green light in a row of five lights? a. 3/16 b. 1/32 c. 5/16 d. 5/32

Answer 1

5/32.

Explanation:

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

As there are 5 lights we need the last row in the above Pascals triangle.

And there is 1 red and 4 green ( = 5) and it can happen in 5 ways, so that gives us the second term in the last row . The total in that last row = 1+5+10+10+5+1 = 32.

so the probability is 5/32.