Answer:
0.9375 ; 0.5
Step-by-step explanation:
Given that :
p = 0.5
Probability model for the Number of girls the couple has :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
P(x = 0) = 4C0 * 0.5^0 * 0.5^4 = 0.0625
P(x = 1) = 4C1 * 0.5^1 * 0.5^3 = 0.25
P(x = 2) = 4C2 * 0.5^2 * 0.5^2 = 0.375
P(x = 3) = 4C3 * 0.5^3 * 0.5^1 = 0.25
P(x = 4) = 4C4 * 0.5^4 * 0.5^0 = 0.0625
Probability of having atleast one girl
Number of trials, n = 4
P(x ≥ 1) = p(x = 1) + p(x = 2) + p(x = 3) + p(x = 4)
Using the relation :
P(x =x) = nCx * p^x * (1 - p)^(n - x)
Using calculator ;
P(x ≥ 1) = 0.9375
Probability of having exactly one boy or exactly one girl
1 boy 3 girls OR 1 girl 3 boys
P(x = 1)
P(x =x) = nCx * p^x * (1 - p)^(n - x)
P(x = 1) = 4C1 * 0.5^1 * 0.5^3
P(x = 1) = 4 * 0.5 * 0.125
P(x = 1) = 0.25
The probability of having one girl, 3 boys and vice versa is 0. 25
Hence, Probability of having exactly one boy or exactly one girl
0.25 + 0.25 = 0.5
