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Home » The probability that an event E occurs in one trial is , Three independent trials of the experiment are performed. What is the probability that E occurs at least once?A. B. C. D. None of these
The probability that an event E occurs in one trial is 0.4, Three independent trials of the experiment are performed. What is the probability that E occurs at least once?
A. 0.784
B. 0.936
C. 0.964
D. None of these
Binomial Distribution | CBSE | Class 12 | Exercise 32A | Maths | RS Aggarwal
The probability that an event E occurs in one trial is 0.4, Three independent trials of the experiment are performed. What is the probability that E occurs at least once?
A. 0.784
B. 0.936
C. 0.964
D. None of these

The probability of occurrence of an event E in one trial is 0.4
Using Bernoulli’s Trial we have,
\begin{array}{l} P(\text { Success }=x)={ }^{n} C_{x} \cdot p^{x} \cdot q^{(n-x)} \\ x=0,1,2, \ldots \ldots \ldots n \text { and } q=(1-p), n=3 \\ p=0.4, q=0.6 \end{array}
The probability that E occurs at least once is,
\begin{array}{l} P(1)+P(2)+P(3) \\ \Rightarrow{ }^{3} C_{1}\left(\frac{2}{5}\right)^{1}\left(\frac{3}{5}\right)^{2}+{ }^{3} C_{2}\left(\frac{2}{5}\right)^{2}\left(\frac{3}{5}\right)^{1}+{ }^{3} C_{3}\left(\frac{2}{5}\right)^{3}\left(\frac{3}{5}\right)^{0} \\ \Rightarrow \frac{98}{125}=0.784 \end{array}
Hence, the correct option is a.

i

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