Consider a standard deck of 52 cards. You select one card at random and do not replace it. You shuffle the deck and then pick another card. If you are trying to find the probability that you pick a Red card first (denoted by R) and then a King card (denoted by K), which of the following probability statements is applicable for finding the probability?

a. P(R )P(K|R)
b. n(R AND K)/n(S)
c. P(R|K )P(K|R)
d. P(R )+P(K)-P(R n K)

a. P(R )P(K|R)

Step-by-step explanation:

The two cards are picked one after the other without replacement.

First card =Red (R)

Second Card=King(K)

The probability we want to find is the conditional Probability of picking a King card GIVEN that a Red Card(R) was already picked.

That is: P(K|R)

For two mutually exclusive events,

P(K|R) = P(K∩R)÷P(R)

Cross Multiplying

P(K∩R)=P(R)P(K|R)

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

graph them on a graphing calculator, press 2nd trace. select intersect. hit enter until it says answer. ti 84 works best

step-by-step explanation: