Question

For the experiment described below, let x determine a random variable, and use your knowledge of probability to prepare a probability distribution. Four cards are drawn (with replacement) and the number of black cards is noted. A probability distribution for the given experiment is as follows. х 0 1 2 3 4 1 16 P(x) 16 4 8

Answer 1

from a deck of 52 cards & cards are drown with replacement. Let X be the number of black cards out of the 4 cards drowon. This is clearly a Binomial experiment because of the following reasons 1 Number of cards drown .e number of trials), u=4 is fixed 2) All the trials of drawing cards are independent and identical. 3) Considering a trial of drawing a card, it results in two outcomes either black Success or red (failure) 4 Probability of getting sa a black card (ie probability of success), p = is same for every trial of drawing a card. 26 tak black and 26 red cards in a deck of playing cards. Now we need to find the following: P(x=0); Formula: P(x=x) = np. av n = 4,x=0, 8= -2, q=1 - P = 1/2 26 52 NOTE: There are xn-d Wen

16 : P(x =0) = 46 (2) (2.) 4 - 0 4 POX=D: P(X=) = 44,5 (4)=40*= P(X=2): PX -2) = 4 ( 5 6 7 8 P(x=3) P(x=3) - 45(50*3=4444= P(x=4): P(X=4) = 4469(234 Probability distribution: ㅗ 16 4 2 Х O Mtt 16 cola P(x) to