Question 1178696
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The number of girls in 10 births is either less than 5, or equal to 5, or more than 5:<br>
P(less than 5 girls)+P(5 girls)+P(more than 5 girls) = 1<br>
Because the probabilities for male or female are the same,<br>
P(less than 5 girls) = P(more than 5 girls)<br>
So<br>
2*P(less than 5 girls) = 1-P(5 girls)
P(less than 5 girls) = (1-P(5 girls))/2<br>
P(5) = C(10,5)*(0.5)^10 = 0.246 (to 3 decimal places)<br>
P(less than 5 girls) = (1-0.246)/2 = 0.377<br>
P(at most 5 girls) = P(less than 5 girls)+P(5 girls) = 0.377+0.246 = 0.623<br>