Answer: 0.3268
Step-by-step explanation:
Given : The number of fireworks are blue = 9
Total remaining = 14
Probability of choosing blue ones[tex]=\dfrac{9}{14}[/tex]
Using binomial probability formula ,
[tex]P(x)=^nC_xp^x(1-p)^{n-x}[/tex], where p is the probability of success in each trial, n is sample size.
If she launches six of them in a random order then n=6.
The probability that exactly 4 of them are blue ones will be :-
[tex]P(x)=^6C_4(\dfrac{9}{14})^4(1-\dfrac{9}{14})^{2}\\\\=\dfrac{6!}{2!4!}(\dfrac{9}{14})^4(\dfrac{5}{14})^{2}\\\\=\dfrac{2460375}{7529536}=0.326763163095\approx0.3268[/tex]
Hence, the required probability = 0.3268
