Suppose that two cards are randomly selected from a standard 52-card deck. (a) what is the probability that the first card is a spadespade and the second card is a spadespade if the sampling is done without replacement? (b) what is the probability that the first card is a spadespade and the second card is a spadespade if the sampling is done with replacement?

a.

b.

Step-by-step explanation:

We are given that two cards are drawn are randomly selected from a standard 52- cards deck.

Total cards=52

Total number of spade cards=13

Probability=

a.The probability of drawing two cards first card is spade and second card is spade without replacement =

The probability of drawing two cards first card is spade and second card is spade=

b. The probability of drawing two cards first is spade and second card is a spade with replacement =

The probability of drawing two cards first is spade and second card is a spade with replacement =

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq