Question 4 (5 marks) The probability distribution table shows the probabilities of having 0, 1, 2 or 3 girls in a family
with 3 children.
1 2 3
3a3aa
P(X - x)
a Find the value for a.
[2]
121
b Find the expected value for the number of girls in a family with 3 children.
In a sample of 400 children, find the expected number of families that have 2 girls.

12

step-by-step explanation:

a triangle's   full angle is 180 degrees so 180 - 156 = 24. 24/2=12

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.