**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

Maths by Mr. M. P. Keshari

Subjects |
Maths (Part-1) by Mr. M. P. Keshari |

Chapter 9 |
Circle |

Chapter 10 |
Tangents to a circle |

Chapter 11 |
Geometrical Construction |

Chapter 12 |
Troigonometry |

Chapter 13 |
Height and Distance |

Chapter 14 |
Mensuration |

Chapter 15 |
Statistics |

Chapter 16 |
Probability |

Chapter 17 |
Co-ordinate Geometry |