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Sagot :
Answer:
[tex]P(x = 1) = 0.3970[/tex]
[tex]P(x = 2) = 0.1307[/tex]
[tex]P(x = 3) = 0.0191[/tex]
[tex]P(x = 4) = 0.0011[/tex]
Step-by-step explanation:
Given
[tex]n =4[/tex]
[tex]p = 0.18[/tex]
Required
(a) - (d)
x | P(x)
0 | 0.452
1 |
2 |
3 |
4 |
To solve (a) to (d), we simply apply the following binomial probability formula
[tex]P(x) = ^nC_xp^x(1-p)^{n-x}[/tex]
Solving (a):
[tex]x = 1[/tex]
So, we have:
[tex]P(x = 1) = ^4C_1 * (0.18)^1 * (1-0.18)^{4-1}[/tex]
[tex]P(x = 1) = ^4C_1 * (0.18)^1 * (1-0.18)^{4-1}[/tex]
[tex]P(x = 1) = 4 * (0.18)^1 * (1-0.18)^3[/tex]
[tex]P(x = 1) = 0.3970[/tex]
Solving (b):
[tex]x = 2[/tex]
So, we have:
[tex]P(x = 2) = ^4C_2 * (0.18)^2 * (1-0.18)^{4-2}[/tex]
[tex]P(x = 2) = 6 * (0.18)^2 * (1-0.18)^2[/tex]
[tex]P(x = 2) = 0.1307[/tex]
Solving (c):
[tex]x = 3[/tex]
So, we have:
[tex]P(x = 3) = ^4C_3 * (0.18)^3 * (1-0.18)^{4-3}[/tex]
[tex]P(x = 3) = 4 * (0.18)^3 * (1-0.18)^1[/tex]
[tex]P(x = 3) = 0.0191[/tex]
Solving (d)
[tex]x = 4[/tex]
So, we have:
[tex]P(x = 4) = ^4C_4 * (0.18)^4 * (1 - 0.18)^{4-4}[/tex]
[tex]P(x = 4) = 1 * (0.18)^4 * (1 - 0.18)^0[/tex]
[tex]P(x = 4) = 0.0011[/tex]
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