Question

hi, can you help me answer this question, please, thank you:)

Answer 1

SOLUTION

(a) The probability of at least 4 girls means the probability of getting 4 girls or the probability of getting 5 girls.

Using binomial probability formula

$^nC_x\times p^x\times q^{n-x}$

Where p is the probability of success,

q = probability of failure

n = number of outcomes

x = number of successful events.

Probability of getting 4 girls means 4 success (4 girls) and 1 failure (1 boy)

So,

$\begin{gathered} ^nC_x\times p^x\times q^{n-x} \\ ^5C_4\times(0.5)^4\times(0.5)^{5-4} \\ ^5C_4\times(0.5)^4\times(0.5)^1 \\ =0.15625 \end{gathered}$

Probability of getting 5 girls means all 5 success (5 girls) and 0 failure (0 boy)

So, we have

$\begin{gathered} ^5C_5\times(0.5)^5\times(0.5)^{5-5} \\ ^5C_5\times(0.5)^5\times(0.5)^0 \\ =0.03125 \end{gathered}$

So, The probability of at least 4 girls becomes

$\begin{gathered} 0.15625+0.03125 \\ =0.1875 \end{gathered}$

Therefore, the answer is 0.1875

(b) Probability of at most 4 girls is 1 - the probability of 5 girls

$P(at\text{ most 4 girls) = 1 - P(5 girls) }$

P(5 girls) = 0.03125

So

$\begin{gathered} P(at\text{ most 4 girls) = 1 - P(5 girls) } \\ P(at\text{ most 4 girls) = 1 - }0.03125 \\ =0.96875 \end{gathered}$

Therefore, the answer is 0.9688 to four decimal places