Question

if n coins are tossed, the probability of x heads or x tails 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 1 head when four fair coins are tossed. the probability of getting 1 head when four fair coins are tossed is
(type an integer or a simplified fraction.)

Explanation:

Step1: Identify row and entry in Pascal's triangle

When $n = 4$ coins are tossed, we look at row number 4 in Pascal's triangle. When we want 1 head, we look at entry number 1 of row 4. In Pascal's triangle, row 4 is 1, 4, 6, 4, 1. The 1 - st entry (counting from 0) is 4.

Step2: Identify row sum

The sum of the entries in row 4 of Pascal's triangle is 1 + 4+6 + 4+1=16.

Step3: Calculate probability

The probability $P$ of getting 1 head when 4 coins are tossed is the fraction with the numerator as the entry number 1 of row 4 and denominator as the sum of row 4. So $P=\frac{4}{16}$.

Step4: Simplify fraction

Simplify $\frac{4}{16}$ to $\frac{1}{4}$.

Answer:

$\frac{1}{4}$