A die is thrown 10 times, the probability that an odd number will come up at least one time is

Question

A die is thrown 10 times, the probability that an odd number will come up at least one time is (A) (1/1024) (B) (1023/1024) (C) (11/1024) (D) (1013/1024)

Tardigrade Admin · Accepted Answer

Given n =10 Probability of odd number, p =1 / 2 ∴ q =1 / 2 Required probability = P ( X ≥ 1) =1- P ( X =0) = 1- 10C0 (1/2) 10-0(1/2)0 =1-1 / 210 =1-1 / 1024 =1023 / 1024

Q. A die is thrown $10$ times, the probability that an odd number will come up at least one time is

$\frac{1}{1024}$

$\frac{1023}{1024}$

$\frac{11}{1024}$

$\frac{1013}{1024}$

Given $n = 10$
Probability of odd number, $p = 1/2$
$∴ q = 1/2$
Required probability $= P (X \geq 1)$
$= 1 - P (X = 0)$
$= 1 -^{10} C_{0} (1/2)^{10 - 0} (1/2)^{0}$
$= 1 - 1/ 2^{10}$
$= 1 - 1/1024$
$= 1023/1024$

Q. A die is thrown 10 times, the probability that an odd number will come up at least one time is

10241​

10241023​

102411​

10241013​