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The probabilities that a husband and wife will be alive 20 years from now are given by 0.8 and 0.9 respectively. What is the probability that in 20 years at least one, will be alive?
- a)0.98
- b)0.02
- c)0.72
- d)0.28
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The probabilities that a husband and wife will be alive 20 years from ...
Probability that at least one will be alive
= 1 - probability that no one will be alive
= 1-(0.2)(0.1)
= 1 - 0.02 = 0.98
= 1 - probability that no one will be alive
= 1-(0.2)(0.1)
= 1 - 0.02 = 0.98
Most Upvoted Answer
The probabilities that a husband and wife will be alive 20 years from ...
Problem:
The probabilities that a husband and wife will be alive 20 years from now are given by 0.8 and 0.9 respectively. What is the probability that in 20 years at least one will be alive?
Solution:
To find the probability that at least one of the husband and wife will be alive in 20 years, we need to consider the complementary event, which is the event that both the husband and wife will not be alive.
Complementary Event:
Let's assume P(H) represents the probability that the husband will be alive in 20 years (given as 0.8) and P(W) represents the probability that the wife will be alive in 20 years (given as 0.9). The complementary event is when both the husband and wife will not be alive.
Calculating the Probability:
To find the probability of the complementary event, we can multiply the probabilities of both the husband and wife not being alive:
P(Complementary Event) = (1 - P(H))(1 - P(W))
Explanation:
The probability that the husband will not be alive is 1 - 0.8 = 0.2.
The probability that the wife will not be alive is 1 - 0.9 = 0.1.
Therefore, the probability of the complementary event is:
P(Complementary Event) = (1 - 0.8)(1 - 0.9) = 0.2 * 0.1 = 0.02
Final Calculation:
To find the probability that at least one of them will be alive, we can subtract the probability of the complementary event from 1:
P(At least one will be alive) = 1 - P(Complementary Event) = 1 - 0.02 = 0.98
Thus, the probability that at least one of the husband and wife will be alive in 20 years is 0.98.
Answer:
The correct answer is option 'A', 0.98.
The probabilities that a husband and wife will be alive 20 years from now are given by 0.8 and 0.9 respectively. What is the probability that in 20 years at least one will be alive?
Solution:
To find the probability that at least one of the husband and wife will be alive in 20 years, we need to consider the complementary event, which is the event that both the husband and wife will not be alive.
Complementary Event:
Let's assume P(H) represents the probability that the husband will be alive in 20 years (given as 0.8) and P(W) represents the probability that the wife will be alive in 20 years (given as 0.9). The complementary event is when both the husband and wife will not be alive.
Calculating the Probability:
To find the probability of the complementary event, we can multiply the probabilities of both the husband and wife not being alive:
P(Complementary Event) = (1 - P(H))(1 - P(W))
Explanation:
The probability that the husband will not be alive is 1 - 0.8 = 0.2.
The probability that the wife will not be alive is 1 - 0.9 = 0.1.
Therefore, the probability of the complementary event is:
P(Complementary Event) = (1 - 0.8)(1 - 0.9) = 0.2 * 0.1 = 0.02
Final Calculation:
To find the probability that at least one of them will be alive, we can subtract the probability of the complementary event from 1:
P(At least one will be alive) = 1 - P(Complementary Event) = 1 - 0.02 = 0.98
Thus, the probability that at least one of the husband and wife will be alive in 20 years is 0.98.
Answer:
The correct answer is option 'A', 0.98.
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The probabilities that a husband and wife will be alive 20 years from now are given by 0.8 and 0.9 respectively. What is the probability that in 20 years at least one, will be alive?a)0.98b)0.02c)0.72d)0.28Correct answer is option 'A'. Can you explain this answer?
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