Jasmine drew triangles on a globe and on a flat map of the world, as shown below.Which is a true statement comparing Jasmine’s t
wo drawings?
A. The angle sum of the triangle on the globe is equal to the angle sum of the triangle on the map.
B. The angle sum of the triangle on the globe is greater than the angle sum of the triangle on the map.
C. The New York to Buenos Aires line and the Paris to Buenos Aires line intersect at only one point on the map and only one point on the globe.
D. There is only one line connecting New York to Paris on the map but more than one line connecting New York to Paris on the globe
A. The angle sum of the triangle on the globe is equal to the angle sum of the triangle on the map.
B. The angle sum of the triangle on the globe is greater than the angle sum of the triangle on the map.
C. The New York to Buenos Aires line and the Paris to Buenos Aires line intersect at only one point on the map and only one point on the globe.
D. There is only one line connecting New York to Paris on the map but more than one line connecting New York to Paris on the globe
1 answer:
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Answer:
(a) The PMF of <em>X</em> is:
(b) The probability that a player defeats at least two opponents in a game is 0.64.
(c) The expected number of opponents contested in a game is 5.
(d) The probability that a player contests four or more opponents in a game is 0.512.
(e) The expected number of game plays until a player contests four or more opponents is 2.
Step-by-step explanation:
Let <em>X</em> = number of games played.
It is provided that the player continues to contest opponents until defeated.
(a)
The random variable <em>X</em> follows a Geometric distribution.
The probability mass function of <em>X</em> is:
It is provided that the player has a probability of 0.80 to defeat each opponent. This implies that there is 0.20 probability that the player will be defeated by each opponent.
Then the PMF of <em>X</em> is:
(b)
Compute the probability that a player defeats at least two opponents in a game as follows:
P (X ≥ 2) = 1 - P (X ≤ 2)
= 1 - P (X = 1) - P (X = 2)
Thus, the probability that a player defeats at least two opponents in a game is 0.64.
(c)
The expected value of a Geometric distribution is given by,
Compute the expected number of opponents contested in a game as follows:
Thus, the expected number of opponents contested in a game is 5.
(d)
Compute the probability that a player contests four or more opponents in a game as follows:
P (X ≥ 4) = 1 - P (X ≤ 3)
= 1 - P (X = 1) - P (X = 2) - P (X = 3)
Thus, the probability that a player contests four or more opponents in a game is 0.512.
(e)
Compute the expected number of game plays until a player contests four or more opponents as follows:
Thus, the expected number of game plays until a player contests four or more opponents is 2.