Possibilities and Probabilities 4.51 If 1 card is drawn from a well shuffed deck
ID: 3283157 • Letter: P
Question
Possibilities and Probabilities 4.51 If 1 card is drawn from a well shuffed deck of 52 playing cards, what playing cards, what are the probabilities of getting (a) a red king; (b) a black card; (c) a 3, 4,5, or 6; (d) a diamond; (e) not a diamond; (f) not an ace? 4.52 If H stands for heads and T for tails, the four possible outcomes for two flins coin are HH, HT, TH, and TT. If it can be assumed that these four possibilities ar equally likely, what are the probabilities of getting 0, 1, or 2 heads? 4.53 If H stands for heads and T for tails, the eight possible outcomes for three flips of a coin are HHH, HHT, HTH, THH, HTT, THT, TTH, and TTT. If it can be assumed that these eight possibilities are equally likely, what are the probabilities of getting 0, 1, 2, or 3 heads? 4.54 A refrigerated case holds 24 cans of soft drinks: 6 cola, 6 root beer, 3 orange, 3 sparkling water, and 6 ginger ale. If one can is drawn at random, what is the probability of getting (a) a can of root beer (b) a can of cola or a can of ginger ale; (c) a can that is neither cola, root beer, nor ginger ale?Explanation / Answer
I am solving the first question (4.51) with multiple sub-parts as per Chegg guidelines, post multiple question to get the remaining answers
Q4.51)
(a) a red king
There are two red kings, one from each red suite.
Hence probability of getting red king = 2C1/52C1 = 2/52 = 1/26
(b) a black card
There are 26 black card, 13 from each black suite.
Hence probability of getting a black card = 26C1/52C1 = 2/52 = 1/2
(c) a 3,4,5,6
There are four cards with numer 3,4,5,6 and each suite will have these four cards, hence total possible cards will be 4 * 4 = 16
Probability of event = 16C1/56C1 = 2/7
(d) a diamond
There will be 13 cards of diamond suite
Probability of getting diamond = 13C1/52C1 = 1/4
(e) not a diamond
P(not a diamond) = 1 - P(diamond) = 1 - 1/4 = 3/4
(f) not an ace
1 Ace is present per suite. hence there will be total of 4 aces
P(not an ace) = 1 - P(Ace) = 1 - 4C1/52C1 = 1 - 1/13 = 12/13