Question

1. A fair coin is flipped four times. Find the probability that exactly two of the flips will turn up as heads.

2. A fair coin is flipped four times. Find the probability that at least two of the flips will turn up as heads.

3. A six-sided dice is rolled twice. Find the probability that the larger of the two rolls was equal to 3.

4. A six-sided dice is rolled twice. Find the probability that the larger of the two rolls was less than or equal to 5.

Answer 1

1. Possible outcomes when a A fair coin is flipped four times

H : Heads

T : Tails

{ HHHH , THHH, HTHH ,HHTH ,HHHT , HHTT ,HTTH , HTHT , TTHH ,THTH ,THHT , TTTH , TTHT , THTT ,HTTT ,TTTT }

Total outcomes = 16

outcomes with exactly 2 heads = 6

( HHTT ,HTTH , HTHT , TTHH ,THTH ,THHT )

Probability = > 6/16

= > 3/8

2. Probability atleast 2 heads

Outcomes with atleast 2 heads = > 6 + 4 + 1 = > 11

Total ouctomes = 16

THHH, HTHH ,HHTH ,HHHT , HHTT ,HTTH , HTHT , TTHH ,THTH ,THHT ,HHHH

Probability = 11/16

3.

Total ouctomes when we roll a dice twice = > 36

cases when larger of the two is 3 = > (1,3) (3,1) (2,3) (3,2) => 4

Probability = > 4/36

= > 1/9

4.

Probability ( larger of the two rolls was less than or equal to 5 ) = 1 - Probability(larger of the two rolls is equal to 6)

cases when larger of the two is 6

( 1,6 )(2,6)(3,6)(4,6)(5,6) and (6,1)(6,2)(6,3)(6,4)(6,5) => 10

Probability(larger of the two rolls is equal to 6) = 10/36

Probability ( larger of the two rolls was less than or equal to 5 ) = 1 - 10/36

= 26/36

= 13/18