Merge pull request #1 from prashantsinalkar/masterHEADmaster

Added R TBC

14 files changed, 136 insertions, 0 deletions

diff --git a/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX3.b/Ex2_3b.R b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX3.b/Ex2_3b.R
new file mode 100644
index 00000000..596369cf
--- /dev/null
+++ b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX3.b/Ex2_3b.R
@@ -0,0 +1,5 @@
+p_of_a_side = 1/6
+no_of_even_sides = 3
+
+ans = p_of_a_side * no_of_even_sides
+print(ans)
\ No newline at end of file
diff --git a/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX4.a/Ex2_4a.R b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX4.a/Ex2_4a.R
new file mode 100644
index 00000000..de77ed08
--- /dev/null
+++ b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX4.a/Ex2_4a.R
@@ -0,0 +1,6 @@
+p_book1 = 0.5
+p_book2 = 0.4
+p_both_books = 0.3
+
+ans = 1 - (p_book1 + p_book2 - p_both_books)
+print(ans)
\ No newline at end of file
diff --git a/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.a/Ex2_5a.R b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.a/Ex2_5a.R
new file mode 100644
index 00000000..3ef6d02c
--- /dev/null
+++ b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.a/Ex2_5a.R
@@ -0,0 +1,9 @@
+#install.packages("MASS")
+require(MASS)
+
+favourable_outcomes = 6
+total_outcomes = 36
+
+ans = favourable_outcomes / total_outcomes
+
+print(fractions(ans))
\ No newline at end of file
diff --git a/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.b/Ex2_5b.R b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.b/Ex2_5b.R
new file mode 100644
index 00000000..d12da2d2
--- /dev/null
+++ b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.b/Ex2_5b.R
@@ -0,0 +1,15 @@
+#install.packages("MASS")
+require(MASS)
+
+total_white_balls = 6
+total_black_balls = 5
+
+fav_no_of_white_balls = 1
+fav_no_of_black_balls = 2
+
+drawn_balls = 3
+
+ans = (choose(total_white_balls, fav_no_of_white_balls) * choose(total_black_balls, fav_no_of_black_balls)) / choose(total_black_balls + total_white_balls, drawn_balls)
+
+print(fractions(ans))
+
diff --git a/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.c/Ex2_5c.R b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.c/Ex2_5c.R
new file mode 100644
index 00000000..74fb3470
--- /dev/null
+++ b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.c/Ex2_5c.R
@@ -0,0 +1,13 @@
+#install.packages("MASS")
+require(MASS)
+total_men = 6
+total_women = 9
+
+fav_no_of_men = 3
+fav_no_of_women = 2
+
+commmittee_size = 5
+
+ans = (choose(total_women, fav_no_of_women) * choose(total_men, fav_no_of_men)) / choose(total_men + total_women, commmittee_size )
+
+print(fractions(ans))
diff --git a/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.f/Ex2_5f.R b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.f/Ex2_5f.R
new file mode 100644
index 00000000..77e130c3
--- /dev/null
+++ b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.f/Ex2_5f.R
@@ -0,0 +1,7 @@
+hand_size = 5
+total_cards = 52
+
+no_of_straights = 10*(4^5 - 4)
+ans = no_of_straights / choose(total_cards, hand_size)
+
+print(ans)
\ No newline at end of file
diff --git a/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.g/Ex2_5g.R b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.g/Ex2_5g.R
new file mode 100644
index 00000000..1de2cab0
--- /dev/null
+++ b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.g/Ex2_5g.R
@@ -0,0 +1,7 @@
+total_hands = 5
+total_cards = 52
+
+total_full_houses = 13*12*choose(4,2)*choose(4,3) 
+ans = total_full_houses / choose(total_cards, total_hands)
+
+print(ans)
diff --git a/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.h.a/Ex2_5ha.R b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.h.a/Ex2_5ha.R
new file mode 100644
index 00000000..df83cf86
--- /dev/null
+++ b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.h.a/Ex2_5ha.R
@@ -0,0 +1,8 @@
+total_cards = 52
+suite_size = 13
+
+p_13spades = 1 / choose(total_cards, suite_size)
+
+ans = 4*p_13spades
+
+print(ans)
diff --git a/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.h.b/Ex2_5hb.R b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.h.b/Ex2_5hb.R
new file mode 100644
index 00000000..2eb08808
--- /dev/null
+++ b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.h.b/Ex2_5hb.R
@@ -0,0 +1,9 @@
+total_cards = 52
+suite_size = 13
+
+no_of_aces = 4
+ace_per_suite = 1
+
+ans = (factorial(no_of_aces)* (factorial(total_cards - no_of_aces)/ factorial(suite_size - ace_per_suite)^4)) / (factorial(total_cards) / factorial(suite_size)^4)
+
+print(ans)
diff --git a/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.i/Ex2_5i.R b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.i/Ex2_5i.R
new file mode 100644
index 00000000..52a7e824
--- /dev/null
+++ b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.i/Ex2_5i.R
@@ -0,0 +1,11 @@
+days_in_a_year = 365
+n = 0
+p = 1
+i = 0
+while(p >= 0.5){
+  p = p*(days_in_a_year - i)/ days_in_a_year
+  n = n + 1
+  i = i + 1
+}
+
+print(n)
\ No newline at end of file
diff --git a/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.k/Ex2_5k.R b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.k/Ex2_5k.R
new file mode 100644
index 00000000..d6546498
--- /dev/null
+++ b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.k/Ex2_5k.R
@@ -0,0 +1,12 @@
+P_2i <- function(i, o = 20, d = 20){
+  k = (factorial(o - 2*i) / (2^(o/2 - i) * factorial(o/2 - i)))^2
+  numer = ((dim(combn(o, 2*i))[2])^2) * factorial(2*i) * k
+  denom = (factorial(o + d) / (2^20 * factorial(o)))
+  return(numer / denom)
+}
+
+for(i in 0:10){
+  cat("P(", i,") =", P_2i(i), "\n")
+}
+
+
diff --git a/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.l/Ex2_5l.R b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.l/Ex2_5l.R
new file mode 100644
index 00000000..2bf7f4d7
--- /dev/null
+++ b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.l/Ex2_5l.R
@@ -0,0 +1,11 @@
+no_tennis = 36
+no_squash = 28
+no_badminton = 18
+no_tennis_badminton = 12
+no_tennis_squash = 22
+no_badminton_squash = 9
+no_all = 4
+
+ans = no_tennis + no_squash + no_badminton - no_badminton_squash - no_tennis_badminton - no_tennis_squash + no_all
+
+print(ans)
\ No newline at end of file
diff --git a/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.n/Ex2_5n.R b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.n/Ex2_5n.R
new file mode 100644
index 00000000..3495b0e6
--- /dev/null
+++ b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX5.n/Ex2_5n.R
@@ -0,0 +1,10 @@
+no_of_couples = 10
+
+ans = 0
+
+for(i in 1:10){
+  ans = ans + ((-1)^(i+1)) * choose(10,i) * (2^i) * factorial(19 - i) / factorial(19)
+}
+
+ans = 1 - ans
+print(ans)
\ No newline at end of file
diff --git a/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX7.a/Ex2_7a.R b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX7.a/Ex2_7a.R
new file mode 100644
index 00000000..b4053813
--- /dev/null
+++ b/A_First_Course_In_Probability_by_Sheldon_Ross/CH2/EX7.a/Ex2_7a.R
@@ -0,0 +1,13 @@
+#P[i] = probability of (i+1)th horse winning
+
+P = c(0.2, 0.2, 0.15, 0.15, 0.1, 0.1, 0.1)
+print(P)
+
+v1 = P[1] + P[2] + P[3]
+print(v1)
+v2 = P[1] + P[5] + P[6] + P[7]
+if(v1 > v2){
+  print("First wager")
+} else{
+  print("Second wager")
+}