Question

If a coin is flipped 10 times, what is the probability that it will show all heads or all tails? A 1/2 B 1/512 C 1/1022 D 1/1024 E 1/2048

Answer 1

The probability of multiple events happening is calculated by multiplying the probabilities of each event together. This is the case if each event is independent of the other events.

For a fair coin, the probability of tails is 1/ 2 or 0.5, so the probability of all tails in 10 tosess is (1/2)^10 = 1/1024 = 0.0009765625

Correct answer: D

Answer 2

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.

$\large { \boxed {P(A) = \frac{\text{Number of Favorable Outcomes to A}}{\text {Total Number of Outcomes}} } }$

Permutation ( Arrangement )

Permutation is the number of ways to arrange objects.

$\large {\boxed {^nP_r = \frac{n!}{(n - r)!} } }$

Combination ( Selection )

Combination is the number of ways to select objects.

$\large {\boxed {^nC_r = \frac{n!}{r! (n - r)!} } }$

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 :

$\boxed {P(H) = \frac{1}{2^{10}}}$

The probability that it will show all tails P(T) is :

$\boxed {P(T) = \frac{1}{2^{10}}}$

The probability that it will show all heads or all tails is :

$P(H \cup T) = P(H) + P(T)$

$P(H \cup T) = \frac{1}{2^{10}} + \frac{1}{2^{10}}$

$P(H \cup T) = \frac{2}{2^{10}}$

$P(H \cup T) = \frac{1}{2^{9}}$

$\large {\boxed {P(H \cup T) = \frac{1}{512}} }$

Learn more

• Different Birthdays : brainly.com/question/7567074
• Dependent or Independent Events : brainly.com/question/12029535
• Mutually exclusive : 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