Three people each flip two fair coins. The probability that exactly two of the people flipped one head and one tail, is

Question

Three people each flip two fair coins. The probability that exactly two of the people flipped one head and one tail, is (A) 1/2 (B) 3/8 (C) 5/8 (D) 3/4

Tardigrade Admin · Accepted Answer

n =3 ; P ( success )= P ( H T or T H )=(1/2) ⇒ p = q =(1/2) and r =2 P ( r =2)= 3 C 2((1/2))2 ⋅ (1/2)=(3/8)

Q. Three people each flip two fair coins. The probability that exactly two of the people flipped one head and one tail, is

1/2

3/8

5/8

3/4

$n = 3; P ($ success $) = P (H$ T or $T H) = \frac{1}{2} \Rightarrow p = q = \frac{1}{2}$ and $r = 2$
$P (r = 2) =^{3} C_{2} (\frac{1}{2})^{2} \cdot \frac{1}{2} = \frac{3}{8}$

Q. Three people each flip two fair coins. The probability that exactly two of the people flipped one head and one tail, is

1/2

3/8

5/8

3/4

n=3;P( success )=P(H T or TH)=21​⇒p=q=21​ and r=2 P(r=2)=3C2​(21​)2⋅21​=83​

$n = 3; P ($ success $) = P (H$ T or $T H) = \frac{1}{2} \Rightarrow p = q = \frac{1}{2}$ and $r = 2$
$P (r = 2) =^{3} C_{2} (\frac{1}{2})^{2} \cdot \frac{1}{2} = \frac{3}{8}$