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Find the probability of at least 2 girls in 7 births. Assume that male and female births are equally likely and the births are independent events.

asked Mar 19, 2015 in STATISTICS by doan12345 Pupil

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Step 1:

Find the probability atleast 2 girls in 7 births.

Probability of female birth is $\small \frac{1}{2}$ .

The probability for k successes is .

Where n is number of samples(trails),

p is probability of success,

q is probability of failure.

Here the number of samples are 7.

Probability of success is $\small \frac{1}{2}$ .

Probability of failure is $\small 1-\frac{1}{2}=\frac{1}{2}$ .

Now probability of atleast 2 girls in 7 births is

$\small \\P(\textup{\textrm{atleast}}\2\ \textup{\textrm{girls}}\ \textup{\textrm{in}} \7\ \textup{\textrm{births}})\\ \\= P(2\ \textup{\textrm{girls}}) + P(3\ \textup{\textrm{girls}}) + P(4\ \textup{\textrm{girls}}) + P(5\ \textup{\textrm{girls}}) + P(6\ \textup{\textrm{girls}}) + P(7\ \textup{\textrm{girls}})\\ \\= 1- \left (P(0\ \textup{\textrm{girls}})+P(1 \ \textup{\textrm{girls}}) \right )\\ \\=1-\left ({^7}C_0 (0.5)^{0}(0.5)^{7}-{^7}C_1(0.5)^{1}(0.5)^{6} \right )\\ \\= 1- 0.0078125-0.0546875\\ \\ =1- 0.0625\\ \\=0.9375$

Probability of atleast 2 girls in 7 births is 0.9375.

Solution:

Probability of atleast 2 girls in 7 births is 0.9375.

answered Mar 19, 2015 by Lucy Mentor
edited Mar 19, 2015 by Lucy

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