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  • The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is A. ^5_C4 (0.7)^4 (0.3) B. 5C1 (0.7) (0.3)4 C. 5C4 (0.7) (0.3)4 D. (0.7)4 (0.3)

The probability that a person is not a swimmer is 0.3. The probability that out of 5 persons 4 are swimmers is
\\A. { }^{5} \mathrm{C}_{4}(0.7)^{4}(0.3) \\B. { }^{5} C_{1}(0.7)(0.3)^{4} \\C. { }^{5} \mathrm{C}_{4}(0.7)(0.3)^{4} \\D.(0.7)^{4}(0.3)

Answers (1)

Given-

Total number of person  n=5

Total number of swimmers among total person , r=4
Probability of not swimmer , Q=0.3
Therefore, The probability of swimmer , p=1-Q=0.7

As we know that the probability distribution \mathrm{P}(\mathrm{X}=\mathrm{r})={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}(\mathrm{p})^{r} \mathrm{q}_{ }^{\mathrm{n-r}}
$$ \\P(X)={ }^{n} C_{r}(p)^{r}(q)^{n-r} \\ \\P(X)=\frac{n !}{(n-r) ! \times r !} \times(p)^{r} \times(q)^{n-r}
=\frac{5 !}{4 ! \times 1 !} \times(0.7)^{4} \times(0.3)
Hence, { }^{5} \mathrm{C}_{4}(0.7)^{4}(0.3)

Option A is correct.

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infoexpert22

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