a game uses a special deck of cards with 40 cards numbered from 1 to 40. you draw a card from the shuffled…

a game uses a special deck of cards with 40 cards numbered from 1 to 40. you draw a card from the shuffled deck. what is the probability of drawing a card that is divisible by 2?

a game uses a special deck of cards with 40 cards numbered from 1 to 40. you draw a card from the shuffled deck. what is the probability of drawing a card that is divisible by 2?

Answer

Explanation:

Step1: Count favorable outcomes

The numbers from 1 - 40 that are divisible by 2 are 2, 4, 6, …, 40. This is an arithmetic - sequence with first term (a = 2), common difference (d = 2) and last term (l=40). Using the formula (l=a+(n - 1)d), we have (40 = 2+(n - 1)\times2). Solving for (n): [ \begin{align*} 40&=2+(n - 1)\times2\ 40&=2 + 2n-2\ n&=20 \end{align*} ] So there are 20 favorable outcomes.

Step2: Calculate probability

The probability (P) of an event is given by the formula (P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}). The total number of outcomes is 40 (since there are 40 cards). So (P=\frac{20}{40}). [P=\frac{20}{40}=\frac{1}{2}]

Answer:

(\frac{1}{2})