1.It is more difficult (i.e. lower probability) to roll 2 dice once and get either a...
1.It is more difficult (i.e. lower probability) to roll 2 dice once and get either a 2 or 12 than it is to draw either an Ace of spades or clubs from a deck of playing cards with only one draw.
True or false, Explain please
Homework Answers
Answer - False
Explanation - Two dice rolled at the same time. Expected outcome is either 2 or 12. Total number of outcomes is 36 as there are 36 combination of outcomes we can get from two dice. So, the probability is 2/36 as we have two outcomes that we are expecting.
Similarly, there are 52 cards in total. The outcome that we are expecting is either Ace of Spades or Ace of Clubs. That means 2 outcomes. The probability is 2/52.
2/36 = 1/18
2/52 = 1/26 (Here, we reduced the fractions to its simplest forms)
By comparing both the fractions, we can determine which one has the lowest probability.
Comparing, 1/18 and 1/26
First, lets take the LCM of 18 and 26.
LCM = 234
Now divide both the denominators with the LCM
234 ÷18 = 13
234 ÷ 26 = 9
Now, multiply 13 with the numerator 1, we get 13
Similarly, multiply 9 with the numerator 1, we get 9.
We can write it like this
1/18 ×13/13 = 13/234
1/26 × 9/9 = 9/234
We can conclude that drawing an ace of clubs or spades from a deck of 52 cards has a lower probability than rolling 2 dice and getting a two or a twelve.
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