Chapter 16: Probability

Example 6. Three unbiased coins are tossed simultaneously. What is the probability of getting exactly two heads?

Solution: - When three coins are tossed simultaneously, the sample space is

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}.

n(S) = 8

E = Set of cases favorable to the event

= {HHT, HTH, THH}

n(E) = 3

P (exactly two heads) =

Example 7. A dice is thrown twice. Find the probability of getting (a) doublets (b) prime number on each die.

Solutions: - Sample space =

S = { (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) }

n (S) = 36

(i) E = Events getting doublet

      = {(1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)}

      n (E) = 6

      P(doublet) =

(ii) E = Events getting prime number on each die.

         = {(2, 2), (2, 3), (2, 5), (3, 2), (3, 3), (3, 5), (5, 2), (5, 3), (5, 5)}

         n(E) = 9

         P (getting prime number on each die)

         = n(E)/n(S) = 9/36 = 1/4