Respuesta :
Answer:
The probability that you lose at most 2 out of your 6 races is 0.54432.
Step-by-step explanation:
We are given that you are running a race. The probability that you win is 3/5.
There are total of 6 races.
The above situation can be represented through binomial distribution;
[tex]P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 6 races
r = number of success = at most 2 lost
p = probability of success which in our question is probability that
you lose a race = 1 - (3/5) = 2/5 or 0.4
Let X = Number of races lost
So, X ~ Binom(n = 6, p = 0.40)
Now, the probability that you lose at most 2 out of your 6 races is given by = P(X [tex]\leq[/tex] 2)
P(X [tex]\leq[/tex] 2) = P(X = 0) + P(X = 1) + P(X = 2)
= [tex]\binom{6}{0} \times 0.40^{0} \times (1-0.40)^{6-0} + \binom{6}{1} \times 0.40^{1} \times (1-0.40)^{6-1} + \binom{6}{2} \times 0.40^{2} \times (1-0.40)^{6-2}[/tex]
= [tex]1 \times1 \times 0.60^{6} + 6 \times 0.40^{1} \times 0.60^{5} +15\times 0.40^{2} \times 0.60^{4}[/tex]
= 0.54432
