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yanalaym [24]
3 years ago
11

Based on the 2009 season, the Texas Rangers have a winning percentage of .533. Use the binomial model to find the probability th

at the Rangers win 4 of their next 5 games.
Mathematics
2 answers:
Naddik [55]3 years ago
8 0

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.

NARA [144]3 years ago
5 0

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 <em>p</em> is the probability of a success and <em>q</em> is the probability of a failure.

q = 1 - p

= 1 - 0.533

= 0.467

Substitute <em>p</em> = 0.533,  <em>q</em> = 0.467 and <em>n</em> = 5, <em>x</em> = 4, we get,

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

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

≅ 0.127

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