The probability that a football game will go into overtime is 10% what is the probability that exactly two ofthree football games will go to into overtime?

Answer 1

# 0.027#.

Let us call going overtime of a football game a success.

Then, the probability (prob.) #p# of success is #p=10%=1/10#, so
that, the prob. #q# of failure is #q=1-p=9/10#.
If, #X=x# denotes the number of football games that go overtime,
then, #X=x# is a Binomial Random Variable with parameters
#n=3, p=1/10, &, q=9/10, i.e., X~B(3,1/10)#.
#:."The Reqd. Prob."=P(X=2)=p(2)#.
We have, for #X~B(n,p),#
#P(X=x)=p(x)=""_nC_xp^xq^(n-x), x=0,1,2,...,n#.
#:."The Reqd. Prob."= P(X=2)=p(2)=""_3C_2(1/10)^2(9/10)^1#,
#=3*1/100*9/10#.
#=0.027#.
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Answer 2

To find the probability that exactly two out of three football games will go into overtime, we can use the binomial probability formula:

P(k successes) = (n choose k) * p^k * (1 - p)^(n - k)

Where:

  • n is the total number of trials (in this case, 3 games)
  • k is the number of successes (in this case, 2 games going into overtime)
  • p is the probability of success on each trial (in this case, 10% or 0.10)

Plugging in the values:

P(2 games in overtime) = (3 choose 2) * (0.10)^2 * (1 - 0.10)^(3 - 2)

Calculating:

P(2 games in overtime) = (3 choose 2) * (0.10)^2 * (0.90)^(3 - 2) = (3! / (2! * (3 - 2)!)) * (0.10)^2 * (0.90)^1 = (3 / 2) * 0.01 * 0.90 = 0.135

So, the probability that exactly two out of three football games will go into overtime is 0.135 or 13.5%.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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