The probability that it will show all heads or all tails is B. 1/512
Further explanation
The probability of an event is defined as the possibility of an event occurring against sample space.
[tex]\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }[/tex]
Permutation ( Arrangement )
Permutation is the number of ways to arrange objects.
[tex]\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }[/tex]
Combination ( Selection )
Combination is the number of ways to select objects.
[tex]\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }[/tex]
Let us tackle the problem.
If a coin is flipped 10 times , then its sample space is : 2¹⁰
The probability that it will show all heads P(H) is :
[tex]\boxed {P(H) = \frac{1}{2^{10}}}[/tex]
The probability that it will show all tails P(T) is :
[tex]\boxed {P(T) = \frac{1}{2^{10}}}[/tex]
The probability that it will show all heads or all tails is :
[tex]P(H \cup T) = P(H) + P(T)[/tex]
[tex]P(H \cup T) = \frac{1}{2^{10}} + \frac{1}{2^{10}}[/tex]
[tex]P(H \cup T) = \frac{2}{2^{10}}[/tex]
[tex]P(H \cup T) = \frac{1}{2^{9}}[/tex]
[tex]\large {\boxed {P(H \cup T) = \frac{1}{512}} }[/tex]
Learn more
- Different Birthdays : https://brainly.com/question/7567074
- Dependent or Independent Events : https://brainly.com/question/12029535
- Mutually exclusive : https://brainly.com/question/3464581
Answer details
Grade: High School
Subject: Mathematics
Chapter: Probability
Keywords: Probability , Sample , Space , Six , Dice , Die , Binomial , Distribution , Mean , Variance , Standard Deviation
