India is the second most populous country in the world, with a population of over 1 billion people. Although the government has offered various incentives for population control, some argue that the birth rate, especially in rural India, is still too high to be sustainable. A demographer assumes the following probability distribution for the household size in India.
Household Size Probability
1 0.02
2 0.09
3 0.18
4 0.25
5 0.20
6 0.12
7 0.08
8 0.06
a. What is the probability that there are less than 5 members in a household in India? (Round your answer to 2 decimal places.)
b. What is the probability that there are 5 or more members in a household in India? (Round your answer to 2 decimal places.)
c. What is the probability that the number of members in a household in India is strictly between 2 and 5? (Round your answer to 2 decimal places.)
a. To find the probability that there are less than 5 members in a household in India, we need to sum the probabilities for household sizes 1, 2, 3, and 4.
P(household size < 5) = P(household size = 1) + P(household size = 2) + P(household size = 3) + P(household size = 4)
= 0.02 + 0.09 + 0.18 + 0.25
= 0.54
So the probability that there are less than 5 members in a household in India is 0.54.
b. To find the probability that there are 5 or more members in a household in India, we need to sum the probabilities for household sizes 5, 6, 7, and 8.
P(household size ≥ 5) = P(household size = 5) + P(household size = 6) + P(household size = 7) + P(household size = 8)
= 0.20 + 0.12 + 0.08 + 0.06
= 0.46
So the probability that there are 5 or more members in a household in India is 0.46.
c. To find the probability that the number of members in a household in India is strictly between 2 and 5, we need to sum the probabilities for household sizes 3 and 4.
P(2 < household size < 5) = P(household size = 3) + P(household size = 4)
= 0.18 + 0.25
= 0.43
So the probability that the number of members in a household in India is strictly between 2 and 5 is 0.43.
To find the probabilities, we can sum up the probabilities for the respective household sizes.
a. To find the probability that there are less than 5 members in a household, we sum up the probabilities for household sizes 1, 2, 3, and 4.
P(X < 5) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
= 0.02 + 0.09 + 0.18 + 0.25
= 0.54
Therefore, the probability that there are less than 5 members in a household in India is 0.54.
b. To find the probability that there are 5 or more members in a household, we sum up the probabilities for household sizes 5, 6, 7, and 8.
P(X ≥ 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8)
= 0.20 + 0.12 + 0.08 + 0.06
= 0.46
Therefore, the probability that there are 5 or more members in a household in India is 0.46.
c. To find the probability that the number of members in a household in India is strictly between 2 and 5, we sum up the probabilities for household sizes 3 and 4.
P(2 < X < 5) = P(X = 3) + P(X = 4)
= 0.18 + 0.25
= 0.43
Therefore, the probability that the number of members in a household in India is strictly between 2 and 5 is 0.43.
To find the probabilities in this problem, you need to sum up the probabilities for the desired events.
a. To find the probability that there are less than 5 members in a household in India, you need to sum up the probabilities for household sizes 1, 2, 3, and 4. So the probability is:
Probability = 0.02 + 0.09 + 0.18 + 0.25 = 0.54
Therefore, the probability that there are less than 5 members in a household in India is 0.54.
b. To find the probability that there are 5 or more members in a household in India, you need to sum up the probabilities for household sizes 5, 6, 7, and 8. So the probability is:
Probability = 0.20 + 0.12 + 0.08 + 0.06 = 0.46
Therefore, the probability that there are 5 or more members in a household in India is 0.46.
c. To find the probability that the number of members in a household in India is strictly between 2 and 5, you need to sum up the probabilities for household sizes 3 and 4. So the probability is:
Probability = 0.18 + 0.25 = 0.43
Therefore, the probability that the number of members in a household in India is strictly between 2 and 5 is 0.43.
In summary:
a. Probability of less than 5 members in a household: 0.54
b. Probability of 5 or more members in a household: 0.46
c. Probability of number of members between 2 and 5: 0.43
Remember to round your answers to 2 decimal places.