Question

There are five different colored cards in a hat. A card is randomly drawn and then replaced. Then a second card is

drawn. What is the probability that the same card will be drawn both times?

4%
20%
25%
5%

Answer 1

4%

Explanation:

Probability Formula

`\sf Probability\:of\:an\:event\:occurring = (Number\:of\:ways\:it\:can\:occur)/(Total\:number\:of\:possible\:outcomes)`

First draw

If there are 5 different colored cards in a hat, the probability of drawing each of the colors on the first draw is the same for each color:

`\implies \textsf{P(one color)}= \sf (1)/(5)`

Second draw

If the first card randomly drawn is replaced, the probability of drawing each of the colors in the second draw is the same as the first draw.

`\implies \textsf{P(one color)}= \sf (1)/(5)`

Both cards the same color

The probability that the same card will be drawn both times is:

`\implies \textsf{P(same card twice)}= \sf (1)/(5) * (1)/(5)=(1)/(25)=0.04=4\%`

Answer 2

• A. 4%

Explanation:

Probability of each card is:

• P(c) = 1/5

Probability of same card the second time is same:

• P(c) = 1/5

Probability of same card twice is:

• P(cc) = 1/5*1/5 = 1/25 = 4%

Correct choice is A