Respuesta :
Answer: The required probability is 0.1144.
Step-by-step explanation:
Since we have given that
Number of married couples = 20
Number of couples who said they paid for their honeymoon = 12
Probability of married couples paid for their honeymoon = 70%
Probability of married couples does not paid for their honeymoon = 30%
So, using "Binomial distribution", we get that
[tex]P(X=12)=^{20}C_{12}(0.7)^{12}(0.30)^8\\\\P(X=12)=0.1144[/tex]
Hence, the required probability is 0.1144.
Answer:
Probability that the number of couples who say they paid for their honeymoon themselves is 12 exactly is 0.1144.
Step-by-step explanation:
We are given that seventy percent of married couples paid for their honeymoon themselves.
You randomly select 20 married couples and ask them if they paid for their wedding themselves.
The above situation can be represented through Binomial distribution;
[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 20 married couples
r = number of success = exactly 12
p = probability of success which in our question is % of married
couples who paid for their honeymoon themselves, i.e; 70%
LET X = Number of couples who say they paid for their honeymoon themselves
So, it means X ~ [tex]Binom(n=20, p=0.70)[/tex]
Now, Probability that the number of couples who say they paid for their honeymoon themselves is 12 exactly is given by = P(X = 12)
P(X = 12) = [tex]\binom{20}{12} \times 0.70^{12} \times (1-0.70)^{20-12}[/tex]
= [tex]125970 \times 0.70^{12} \times 0.30^{8}[/tex]
= 0.1144
Therefore, Probability that the number of couples who say they paid for their honeymoon themselves is 12 exactly is 0.1144.
