Question

Based on the 2009 season, the Texas Rangers have a winning percentage of .533. Use the binomial model to find the probability that the Rangers win 4 of their next 5 games.

Answer 1

Answer:

0.128

Step-by-step explanation:

We know the probability for any event X is given by,

$P(X=x)=\binom{n}{x}\times p^{n-x}\times q^{x}$,

where p is the probability of success and q is the probability of failure.

Here, we are given that p = 0.533.

Since, we have that q = 1 - p

i.e. q = 1 - 0.533

i.e. q = 0.467

It is required to find the probability of 4 wins in the next 5 games i.e. P(X=4) when n = 5.

Substituting the values in the above formula, we get,

$P(X=4)=\binom{5}{4}\times 0.533^{5-4}\times 0.467^{4}$

i.e. $P(X=4)=5 \times 0.533 \times 0.048$

i.e. $P(X=4)=5 \times 0.533 \times 0.048$

i.e. i.e. $P(X=4)=0.128$

Hence, the probability of 4 wins in the next 5 games is 0.128.

Answer 2

Answer:

The required probability is 0.127.

Step-by-step explanation:

The binomial model is given by:

$P(X = x)=nC_{x}p^{n-x} q^{x}$

where p is the probability of a success and q is the probability of a failure.

q = 1 - p

= 1 - 0.533

= 0.467

Substitute p = 0.533,  q = 0.467 and n = 5, x = 4, we get,

$P(X=4)=5C_{4}(0.533)^{1}(0.467)^{4}$

$=5(0.533)(0.467)^{4}$

≅ 0.127