Jessica conducts an experiment. She flips a coin 100 times. In her experiment she gets heads 40 times and tails 60 times. Based
2 answers:
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Answer:
a) The expected number of goals team A will score is 5.1
b) The probability that team A will score a total of 5 goals is 0.1147
Step-by-step explanation:
Let X be the amount of goals scored by team A in both matches. Let X1 and X2 be the total amount of goals team A scores in match 1 and 2 respectively, then X = X1+X2, and also
a)
E(X) = E(X1+X2) = E(X1)+E(X2) = 0.6*2+0.4*3 + 0.3*2+0.7*3 = 5.1
b) In order for X to be equal to 5 we have 5 possibilities
- X1 is 0 and X2 is 5
- X1 is 1 and X2 is 4
- X1 is 2 and X2 is 3
- X1 is 3 and X2 is 2
- X1 is 4 and X2 is 1
- X1 is 5 and X2 is 0
Let T1 be a poisson distribution with mean λ = 2, then
Lets do the same with a Poisson distribution T2 with mean λ = 3
Now, we are ready to compute the probability that X is equal to 5.
We can conclude that
P(X = 5) = 0.00823+0.03214+0.05317+0.0471+0.0225+0.0047 = 0.1147
The probability that team A will score a total of 5 goals is 0.1147