He two-way table shows the medal count for the top-performing countries in the 2012 Summer Olympics.
2 answers:
Answer:
The 1st statement i.e. "The probability that a randomly selected silver medal was awarded to Great Britain is StartFraction 17 Over 99 EndFraction" is true.
Step-by-step explanation:
<em>The</em><em> </em><em> table:</em>
Gold Silver Bronze Total
United States 46 29 29 104
China 38 27 23 88
Russia 24 26 32 82
Great Britain 29 17 19 65
Total 137 99 103 339
Let S be the sample space and E be the event and P(E) by the probability of a certain event.
1st Statement: The probability that a randomly selected silver medal was awarded to Great Britain is StartFraction 17 Over 99 EndFraction.
As the total number of silver medals are = n(S) = 99
The number of silver medals won by Great Britain = n(E) = 17
P(E) = n(E)/n(S) = 17/99
Hence, the probability that a randomly selected silver medal was awarded to Great Britain is 17/99.
So, the 1st statement i.e. "The probability that a randomly selected silver medal was awarded to Great Britain is StartFraction 17 Over 99 EndFraction" is true.
2nd Statement: The probability that a randomly selected medal won by Russia was a bronze medal is StartFraction 32 Over 103 EndFraction.
As the total number of medals won by Russian are = 82 = n(S) = 82
The number of bronze medals won by Russia are = n(E) = 32
P(E) = n(E)/n(S) = 32/82 = 16/41
Hence, the probability that a randomly selected medal won by Russia was a bronze medal is 16/41.
So, the 2nd statement i.e. "The probability that a randomly selected medal won by Russia was a bronze medal is StartFraction 32 Over 103 EndFraction" is NOT true.
3rd Statement: The probability that a randomly selected gold medal was awarded to China is StartFraction 88 Over 137 EndFraction.
As the total number of gold medals are = n(S) = 137
The number of gold medals won by China are = n(E) = 38
P(E) = n(E)/n(S) = 38/137
Hence, the probability that a randomly selected gold medal was awarded to China is 38/137.
So, the 3rd statement i.e. "The probability that a randomly selected gold medal was awarded to China is StartFraction 88 Over 137 EndFraction" is NOT true.
4th Statement: The probability that a randomly selected medal won by the United States was a silver medal is StartFraction 104 Over 339 EndFraction.
As the total number of medals won by United States are = n(S) = 104
The number of silver medals won by United States are = n(E) = 29
P(E) = n(E)/n(S) = 29/104 = 29/104
Hence, The probability that a randomly selected medal won by the United States was a silver medal is 29/104.
So, the 4th statement i.e. "The probability that a randomly selected medal won by the United States was a silver medal is StartFraction 104 Over 339 EndFraction." is NOT true.
Keywords: Probability, event
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