KCET · Maths · Probability
A die is thrown 10 times, the probability that an odd number will come up at least one time is
- A \(\frac{1}{1024}\)
- B \(\frac{1023}{1024}\)
- C \(\frac{11}{1024}\)
- D \(\frac{1013}{1024}\)
Answer & Solution
Correct Answer
(B) \(\frac{1023}{1024}\)
Step-by-step Solution
Detailed explanation
A die is thrown 10 times Probability of success is an odd number \(\therefore \quad n=10, p=\frac{1}{2}, q=\frac{1}{2}\)
Number of success is atleast one Required probability \(P(x \geq 1)=1-P(x=0)\)
\(=1-{ }^{10} C_{0}\left(\frac{1}{2}\right)^{0}\left(\frac{1}{2}\right)^{10}\)
\(=1-\frac{1}{1024}=\frac{1023}{1024}\)
Number of success is atleast one Required probability \(P(x \geq 1)=1-P(x=0)\)
\(=1-{ }^{10} C_{0}\left(\frac{1}{2}\right)^{0}\left(\frac{1}{2}\right)^{10}\)
\(=1-\frac{1}{1024}=\frac{1023}{1024}\)
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