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24 March, 04:04

A couple plans to have no more than three children, and they will keep having children until they have a girl. So, if their first child is a girl, they will stop and have only one child. However, if their first child is a boy, they will try again and have a second child. As it turns out, the probability of having a boy is slightly greater than having a girl. Here is the probability distribution for the number of boys the couple could have. Boys 0 boys 1 boy 2 boys 3 boys Probability 0.490 0.250 0.127 0.133

What is the expected number of boys the couple will have? (Recall: the expected value is the mean). 0.903 1.5 0.228

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  1. 24 March, 04:08
    0
    0.903.

    Step-by-step explanation:

    Okay, from the question we are given the following information or data or parameters:

    ''couple plans to have no more than three children, and they will keep having children until they have a girl. So, if their first child is a girl, they will stop and have only one child"

    Additionally, from the question we are given that; ''However, if their first child is a boy, they will try again and have a second child".

    Also, the probability distribution is given as Boys 0, boys 1, boy 2, boys 3 boys with Probability 0.490, 0.250, 0.127, 0.133 respectively.

    That is, we now have:

    Number of boys * probability.

    Boys 0 = 0 * 0.490 = 0.

    Boys 1 = 1 * 0.250 = 0.250.

    Boys 2 = 2 * 0.127 = 0.254.

    Boys 3 = 3 * 0.133 = 0.399.

    The addition of the products for each Number of boys * probability gives us the expected value. That is to say;

    0 + 0.250 + 0.254 + 0.399 = 0.903 = mean.
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