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Let X represent the number of children in an Australian household. The probability distribution of X is as follows:x12345p(x)0.250.330.170.150.10What is the probability that a randomly selected Australian household will have fewer than 4 children?

Question

Let X represent the number of children in an Australian household. The probability distribution of X is as follows:x12345p(x)0.250.330.170.150.10What is the probability that a randomly selected Australian household will have fewer than 4 children?

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Solution

To find the probability that a randomly selected Australian household will have fewer than 4 children, we need to add up the probabilities for households with 1, 2, and 3 children.

From the given probability distribution:

  • The probability (p(x)) that a household has 1 child (x=1) is 0.25.
  • The probability (p(x)) that a household has 2 children (x=2) is 0.33.
  • The probability (p(x)) that a household has 3 children (x=3) is 0.17.

So, the probability that a household has fewer than 4 children is the sum of these probabilities:

0.25 (for 1 child) + 0.33 (for 2 children) + 0.17 (for 3 children) = 0.75

So, the probability that a randomly selected Australian household will have fewer than 4 children is 0.75 or 75%.

This problem has been solved

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