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mamaluj [8]
3 years ago
6

In a county containing a large number of rural homes, 60% of the homes are insured against fire. Four rural homeowners are chose

n at random from this county, and x are found to be insured against fire. Find the probability distribution for x.
Mathematics
1 answer:
Ray Of Light [21]3 years ago
5 0

Answer:

\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}

Step-by-step explanation:

Given

p = 60\%

n = 4

Required

The distribution of x

The above is an illustration of binomial theorem where:

P(x) = ^nC_x * p^x *(1 - p)^{n-x}

This gives:

P(x) = ^4C_x * (60\%)^x *(1 - 60\%)^{n-x}

Express percentage as decimal

P(x) = ^4C_x * (0.60)^x *(1 - 0.60)^{n-x}

P(x) = ^4C_x * (0.60)^x *(0.40)^{4-x}

When x = 0, we have:

P(x=0) = ^4C_0 * (0.60)^0 *(0.40)^{4-0}

P(x=0) = 1 * 1 *(0.40)^4

P(x=0) = 0.0256

When x = 1

P(x=1) = ^4C_1 * (0.60)^1 *(0.40)^{4-1}

P(x=1) = 4 * (0.60) *(0.40)^3

P(x=1) = 0.1536

When x = 2

P(x=2) = ^4C_2 * (0.60)^2 *(0.40)^{4-2}

P(x=2) = 6 * (0.60)^2 *(0.40)^2

P(x=2) = 0.3456

When x = 3

P(x=3) = ^4C_3 * (0.60)^3 *(0.40)^{4-3}

P(x=3) = 4 * (0.60)^3 *(0.40)

P(x=3) = 0.3456

When x = 4

P(x=4) = ^4C_4 * (0.60)^4 *(0.40)^{4-4}

P(x=4) = 1 * (0.60)^4 *(0.40)^0

P(x=4) = 0.1296

So, the probability distribution is:

\begin{array}{cccccc}x & {0} & {1} & {2} & {3} & {4} \ \\ P(x) & {0.0256} & {0.1536} & {0.3456} & {0.3456} & {0.1296} \ \end{array}

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