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.
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
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