Question

multiple choice 1 point
odds are defined as the number of ways an event will occur compared to the number of ways that event will not occur
1 card is drawn from a standard deck of 52 playing cards.
let event e = the card is not a king
find the odds that the card is not a king.
1:13
13:1
1:12
12:1
fill in the blank 1 point
in california, each license plate consists of a 3 digits, followed by 2 letters, followed by 2 digits.
how many distinct license plates can be formed if there are no restrictions on the digits or letters?
type your answer...

Explanation:

Question 42

Step1: Calculate number of non - King cards

A standard deck has 52 cards. There are 4 Kings. So the number of non - King cards \(n(E)=52 - 4=48\).

Step2: Calculate number of King cards

The number of King cards \(n(\text{not }E)=4\).

Step3: Calculate the odds

Odds of event \(E\) (card is not a King) is \(\frac{n(E)}{n(\text{not }E)}=\frac{48}{4}=\frac{12}{1}\)

Step1: Calculate number of possibilities for digits

For each of the 3 initial digits and 2 final digits, there are 10 possibilities (0 - 9). So for the 3 + 2=5 digit positions, the number of digit combinations is \(10\times10\times10\times10\times10 = 10^{5}\)

Step2: Calculate number of possibilities for letters

For each of the 2 letter positions, there are 26 possibilities (A - Z). So the number of letter combinations is \(26\times26=26^{2}\)

Step3: Calculate total number of license plates

Using the multiplication principle, the total number of license plates is \(10^{5}\times26^{2}\)

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Answer:

\(12:1\)

Question 43