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Nikki2807
07.12.2019 •
Mathematics
An insurance sales representative sells policies to 5 men, all of identical age and in good health. according to the actuarial tables, the probability that a man of this particular age will be alive 30 years hence is . find the probability that in 30 years (a) all 5 men, (b) at least 3 men, (c) only 2 men, (d) at least 1 man will be alive
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Ответ:
(a)![\frac{32}{243}](/tpl/images/0407/2368/93303.png)
(b)![\frac{192}{243}](/tpl/images/0407/2368/3d28e.png)
(c)![\frac{40}{243}](/tpl/images/0407/2368/78c4b.png)
(d)![\frac{242}{243}](/tpl/images/0407/2368/ed214.png)
Additional Information:
An information is missing in the given question. The probability that a man of this particular age will be alive 30 years hence is
. This additional information will be used to solve the question.
Step-by-step explanation:
Let the probability that one person will be alive in 30 years be p
Let the probability that one person will not be alive in 30 years be q
q = 1 - p
The probability function is;
p(x) = ⁿCₓ × pˣ × q⁽ⁿ⁻ˣ⁾
(a) The probability that all 5 men will be alive in 30 years:
p(x=5) = ⁵C₅ ×
× ![(\frac{1}{3})^{5-5}](/tpl/images/0407/2368/cec6e.png)
= (1 ×
× 1)
(b) The probability that at least 3 men will be alive in 30 years:
p(x≥3) = ⁵C₃ ×
×
+ ⁵C₄ ×
×
+ ⁵C₅ ×
× ![(\frac{1}{3})^{5-5}](/tpl/images/0407/2368/cec6e.png)
p(x≥3) = (10 ×
×
) + (5 ×
×
) + (1 ×
× 1)
p(x≥3)
+
+
)
p(x≥3)![=\frac{192}{243}](/tpl/images/0407/2368/9f4d8.png)
(c) The probability that only 2 men will be alive in 30 years:
p(x=2) = ⁵C₂ ×
× ![(\frac{1}{3})^{5-2}](/tpl/images/0407/2368/b5162.png)
p(x=2) = (10 ×
×
)
p(x=2) =![\frac{40}{243}](/tpl/images/0407/2368/78c4b.png)
(d) The probability that at least 1 men will be alive in 30 years:
p(x≥1) = ⁵C₁ ×
×
× ⁵C₂ ×
×
× ⁵C₃ ×
×
+ ⁵C₄ ×
×
+ ⁵C₅ ×
× ![(\frac{1}{3})^{5-5}](/tpl/images/0407/2368/cec6e.png)
p(x≥1) = (5 ×
×
) × (10 ×
×
) × (10 ×
×
) + (5 ×
×
) + (1 ×
× 1)
p(x≥1)
+
+
+
+ ![\frac{32}{243}](/tpl/images/0407/2368/93303.png)
p(x≥1)
Ответ:
25.3 × is the equivalent expression
Step-by-step explanation: