Test Index

Probability

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Question : 77 of 127

Marks: +1, -0

There are three persons aged

60,65

and 70 years old. The survivals probabilities for these three persons for another 5 years are

0.7,0.4

0.2

respectively. What is the probability that at least two of them would survive another five years?

$0.425$
$0.456$
$0.392$
$0.388$

Solution:

Concept:

Calculate probability of at least two survivors using independence.

Explanation:

Let

p_{60}=0.7

,

p_{65}=0.4

,

p_{70}=0.2

.

Probability all three survive:

0.7 \times 0.4 \times 0.2 = 0.056

.

Probability exactly two survive:

• 60 and 65 survive, 70 dies:

0.7 \times 0.4 \times 0.8 = 0.224

• 60 and 70 survive, 65 dies:

0.7 \times 0.6 \times 0.2 = 0.084

• 65 and 70 survive, 60 dies:

0.3 \times 0.4 \times 0.2 = 0.024

Sum exactly two:

0.224+0.084+0.024=0.332

.

Total at least two:

0.332+0.056=0.388

.

Answer:

0.388

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