Question

What is the probability of drawing a diamond or a spade card from a standard deck of cards and rolling a 2 on a six-sided die?10.7%, 25%, 8.3% or4.2%

Answer 1

Let's find the probability of drawing a diamond or a spade card from a standard deck of cards and rolling a 2 on a six-sided die.

Where:

• Number of diamonds in a deck of cards = 13

,

• Number of spade cards in a deck of cards = 13

,

• Total number of cards in a standard deck = 52

,

• Number of 2 on a six-sided die = 1

To find the probability of drawing a diamond or a spade card from a standard deck of cards and rolling a 2 on a six-sided die, apply the formula:

P(diamond or spade and rolling a 2) = P(diamond or spade) or P(2)

Thus, we have:

`\begin{gathered} P(\text{diamond or spade)=}P(\text{diamond) + P(spade) = }(13)/(52)+(13)/(52)=(26)/(52)=(1)/(2) \\ \\ P(\text{rolling a 2) = }(1)/(6) \end{gathered}`

Therefore, we have:

`P(\text{diamond or spade) and P(2) = P}(\text{diamond or spade)}\ast P(2)=(1)/(2)*(1)/(6)=(1)/(12)=0.083`

Therefore, the probability is: = 0.083

Let's convert to percent by mutiplying thr probability by 100:

`0.083*100=8.3\text{ \%}`

ANSWER:

8.3%