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1 Probability

In a binomial distribution consisting of 5 independent trials, the probability of 1 and 2 successes are 0.4096 and 0.2048 respectively. The parameter p of the distribution is

1) $$1/3$$
2) $$1/4$$
3) $$1/5$$
4) None of these

Option 1

Option 2

Option 3 Solution:

Solution

In a binomial distribution consisting of 5 independent trials, n = 5
The probability of 1 and 2 successes are 0.4096 and 0.2048 respectively.
$$ ^{5}C_{1}{ p }^{ 1 }{ (1-p) }^{5-1 } = 0.4096$$ $$ ^{5}C_{2}{ p }^{2 }{ (1-p) }^{5-2 } = 0.2048 $$
$$ 5 { p }{ (1-p) }^{4} = 0.4096$$ _____ (1) $$ 10 { p }^{ 2 }{ (1-p) }^{3} = 0.2048 $$ ______ (2)
Divide equation (1) by (2), we get
$$ \dfrac {(1-p)}{2p} = 2 $$

$$ 5p = 1 $$

$$ p = \dfrac {1}{5} $$

Option 4

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