Question

if n coins are tossed, the probability of x heads is the fraction whose numerator is entry number x of row number n in pascals triangle, and whose denominator is the sum of the entries in row number n. the topmost row of the triangle is
ow number 0\ and the leftmost entry of each row is \entry number 0.\ use the pattern in pascals triangle to find the probability of getting 7 heads when eight fair coins are tossed. the probability of getting 7 heads when eight fair coins are tossed is . (type an integer or a simplified fraction.)

Explanation:

Step1: Identify row and entry in Pascal's triangle

We are tossing 8 coins, so we look at row number 8. We want the probability of 7 heads, so we look at entry number 7 of row 8. In Pascal's triangle, row 8 is 1, 8, 28, 56, 70, 56, 28, 8, 1. The 7 - th entry (counting from 0) is 8.

Step2: Identify row sum

The sum of the entries in row 8 of Pascal's triangle is 256.

Step3: Calculate probability

The probability $P$ of getting 7 heads when 8 coins are tossed is the ratio of the entry number 7 of row 8 to the sum of row 8. So $P=\frac{8}{256}$.

Step4: Simplify the fraction

$\frac{8}{256}=\frac{1}{32}$.

Answer:

$\frac{1}{32}$